Find the exponential growth function, in the form A = Ae", for a city whose population was 34,600 in 1996 and 39,800 in 1999. Use t=0to represent the year 1996. Then, use the growth function to predict
the population of the city in 2006. Round to the nearest hundred.
Answers
Rounding to the nearest hundred, the predicted population of the city in 2006 is 51,100.
To find the exponential growth function, we need to determine the values of A and r in the equation A = Ae^(rt), where A is the initial population and r is the growth rate.
Given that the population was 34,600 in 1996 (t = 0) and 39,800 in 1999 (t = 3), we can set up two equations:
34,600 = A * e^(0 * r)
39,800 = A * e^(3 * r)
Simplifying the first equation, we have:
34,600 = A * e^0
34,600 = A
Substituting A = 34,600 into the second equation:
39,800 = 34,600 * e^(3r)
Dividing both sides by 34,600:
1.1503 = e^(3r)
Taking the natural logarithm of both sides:
ln(1.1503) = ln(e^(3r))
ln(1.1503) = 3r
Now, we can solve for r:
r = ln(1.1503) / 3 ≈ 0.0391
So, the growth rate is approximately 0.0391.
Now, we can use the growth function to predict the population in 2006 (t = 10):
A = 34,600 * e^(0.0391 * 10)
Calculating this, we get:
A ≈ 34,600 * e^(0.391) ≈ 34,600 * 1.479 ≈ 51,037.4
Rounding to the nearest hundred, the predicted population of the city in 2006 is 51,100.
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Related Questions
2 divided by 4/5 please help it is due it two minutes please helppppp
Answers
Answer: 25/4
Step-by-step explanation:
2 / 4/5 = 2*5/4 = 25/4
To divide fractions, multiply by the reciprocal of the fraction (flip the numerator and denominator, basically)
Answer:
\(\frac{5}{2}\)
Step-by-step explanation:
\(2\div \frac{4}{5} =\frac{2}{1}\div \frac{4}{5} =\frac{2}{1}\times \frac{5}{4} =\frac{5}{2}\)
Hope I helped you!
a, (2x-2)(x-3)-2(x-2)^2
B,2(4x^3)-(2x+3)(4x^2-6x+9)
C,(4x-1)^3-(4x-3)(16x^2+3)
Answers
Answer:
b I'm pretty sure
Step-by-step explanation:
because I did the math and it shows that's correct
christina, a restaurant manager, would like to make the claim that the average number of customers that her restaurant serves per hour is more than 57. christina samples 29 hours over the course of a week and records the number of customers served and obtains a sample mean of 62 customers per hour.at the 2.5% significance level, should christina reject or fail to reject the null hypothesis given the sample data below?
Answers
Reject the null hypothesis because \($p$\)-value \($=0.0045$\) is less than the Significance level x=0.025.
What is Null Hypothesis ?The null hypothesis is a widely used statistical theory that states that for any given single observable variable, there is no statistical relationship or significance between any two sets of observed data and measured events.
According to the given information
\(& H_0: \mu=57 \\\)
\(& H_a ; \mu > 57 \\\)
\(& \alpha=0.025 \\\)
\(& \text { Test Statistic }=2.61\)
So,
This is right tailed test
\(& \text { Using } z \text { table } \\\)
\(& p(z > 2.61) \\\)
\(&= 1-p(z < 2.61) \\\)
\(&= 1-0.9955 \\\)
\(& p \text {-value }= 0.0045\)
Reject the null hypothesis because \($p$\)-value \($=0.0045$\) is less than the Significance level x=0.025.
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A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade?
Answers
Answer:
The answer is 9295
Step-by-step explanation:
Solution
A poker hands contains of =5 cards
Ordinary deck of =52 cards
Now we need to find the number of hands are there consisting of four hearts and one spade
Thus
The number of ways to get 4 hearts = ¹³C₄
=715
The number of ways to get to 1 spade = ¹³C₁
=13
Then
The total number of ways is given as:
715 * 13 =9295
Therefore, the different hands that are available or present consisting of four hearts and one spade is 9295
What is Santon’s goal?
Answers
Anno one came answer that without numbers
Step-by-step explanation:
Answer:
Although Stanton remained committed to efforts to gain property rights for married women and ending slavery, the women's suffrage movement increasingly became her top priority. Stanton met Susan B
Step-by-step explanation:
A delivery company samples 500 orders and records how many deliveries were early (before quoted delivery date, yes or no). Out of 500 records, 300 of them were delivered early. The company is interested in seeing if they have statistical evidence that they deliver early a majority of the time. a. Write down the null and alternative hypothesis using proper notation. b. What is the estimate of the true proportion of all orders that are delivered early? c. Using R, conduct the hypothesis test to address the goal of the company. State the p-value edo. i and make a conclusion.
Answers
(a) The null and alternative hypothesis using proper notation is
H(0) :p ≤ 0.5
H(1) : p > 0.5
(b) The estimate of the true proportion of all orders that are delivered early is 0.6.
A delivery company samples 500 orders.
Out of 500 records, 300 of them were delivered early.
(a) To determine if the true proportion of orders that were delivered early occurs most of the time or not, i.e., whether the true proportion of orders that were delivered early is more than 0.5, we will perform a one proportion z-test.
Let p stand for the actual ratio. Our theory is stated as follows:
H(0) :p ≤ 0.5
H(1) : p > 0.5
We specifically want to determine whether the true proportion is greater than 0.5, hence this is a right-tailed test.
(b) The sample proportion's estimated value is provided as
P = Number of people who wake up early/Total Number of people
P = 300/500
P = 0.6
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Which of the following is most likely the next step in the series?
A.
B.
C.
D.
Answers
Answer:
B
Step-by-step explanation:
each time the step changes, the amount of vertices(points) increases by 1. the last number of points was 4, so if you increase 4 by 1 you will get 5. figure B has 5 points!
Answer:
Option B
Step-by-step explanation:
With the circle series, there is a figure with an increasing number of points that are on the circle.
Circle one has two dots, circle two has three dots, circle three has four dots, etc.
It would make the most sense if the circle in the next series have five dots.
Option B should be the correct answer.
.In a multiple regression model, the variance of the error term `eâ is assumed to be the same for all values of the dependent variable.
A)the same for all values of the independent variable
B)zero.
C)the same for all values of the independent variable.
D)one.
Answers
In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.
In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.
The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.
The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.
This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).
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Can you help me solve this!
Answers
Hello!
surface area
= 2(6*2) + 2(4*2) + 4*6
= 2*12 + 2*8 + 24
= 24 + 16 + 24
= 64 square inches
Tanya buys 12 water bottles. Of these bottles, 5 hold 300 milliliters each and 7 hold 1.5 liters each. Part A How much water, in milliliters, does Tanya buy? Enter your answer in the box. Part B How much water, in liters, does Tanya buy? Enter your answer in the box.
Answers
Answer:
A- 12,000ml
B- 12l
Step-by-step explanation:
To find milliliters:
1.5l = 1500ml
300(5) + 1500(7) = (1500 + 10500 =) 12,000ml
To find liters:
300 ml = 0.3l
0.3(5) + 1.5(7) = (1.5 + 10.5 =) 12L
Hope this helps!
Which point is a point where the graph of y= (x + 2)(x2 + 4x+3) crosses the x-axis?
A. (-3,0)
B. (2,0)
C. (1,0)
D. (3,0)
Answers
Answer:
A. (-3, 0)
Step-by-step explanation:
There should seemingly be 3 points where this graph crosses the x-axis. To determine each of them we can respectively set y to 0;
0 = (x+2)(x^2 + 4x + 3),
A quick way we can factor x^2 + 4x + 3 is using Vieta's Theorem. I don't ideally use it but since x1 * x2 = 3, and x1 + x2 = - 4 then x1 = -1 and x2 = -3. Since these are the roots the factored expression should be (x + 1)(x + 3).
0 = (x+ 2)(x +1)(x + 3),
x = -2, x= - 1, x= - 3
So the x-intercepts are (-2,0), (-1, 0), and (-3,0)
Your answer is option a
-4×(-2)[2×(-6)+3×(2×6-4-4)]
Answers
\(\large{\underline {\underline {\frak {SolutioN:-}}}}\)
➝ -4 × (-2) [2 × (-6)+ 3×(2×6-4-4) ]
➝ -4 × (-2) [2 × (-6) + 3 × (12-4-4) ]
➝ -4 × (-2) [2 × (-6) + 3 × (12-8) ]
➝ -4 × (-2) [2 × (-6) + 3 × (4) ]
➝ -4 × (-2) [2 × (-6) + 12 ]
➝ -4 × (-2) [(-12) + 12 ]
➝ -4 × (-2) [0]
➝ -4 × 0
➝ 0
Answer:
-4*-2
Step-by-step explanation:
the multiple of both side is 4*2*,26+*32*--=6 44
Along the U.S. Atlantic coast, the sea level is rising about 2 millimeters per year. Joe is 13 years old. How many millimeters has sea level risen since Joe was born?
Answers
Because 2mm x 13 years = 26
An airplane flies with a constant speed of 620 miles per hour. How far can it travel in 2 hours 30 minutes?
Answers
Answer:
1550 miles
Step-by-step explanation:
rate * time = distance
620 m/hr * 2.5 hr = 1550 miles
(Note that 2 hr and 30 min is 2 and 1/2 hours = 2.5 hours)
Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet
longer than it is wide.
Answers
The equation to determine the length and width of the rug is
28 = w² + 12w
Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.
What is a rectangle?
Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
We are given a rectangular rug with an area of 28 square feet.
Also, the rug is 12 feet longer than it is wide.
So,
Let 'l' be the length of the rug and 'w' be the width of the rug
As given, Length is 12 feet longer than its width
Therefore, l = w + 12
We know Area of rectangle = Length * Width and area is given to be 28 square feet.
So,
⇒28 = (w + 12)w
⇒28 = w² + 12w
Hence, the equation to determine the length and width of the rug is
28 = w² + 12w.
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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.
Create an equation to determine the length and the width of the rug.
If your initial principal is $243 and your principal in 2 years is $1,359.19, how much interest did you earn?
Answers
Answer: $1,116.19
Step-by-step explanation:
If you invested $243 and this increased to $1,359.19 in two years, the difference between your investment and its current worth is the interest:
= Current principal - Initial principal
= 1,359.19 - 243
= $1,116.19
a rectangle is inscribed in a right isosceles triangle with a hypotenuse of length 6 units. what is the largest area the rectangle can have?
Answers
Answer: The largest area of a rectangle is 32 square units. A rectangle has its base on x-axis and its upper two vertices on the parabola y= 12 - x^2.
Step-by-step explanation:
This is the answer
What is the value of x in the equation One-third x minus two-thirds = negative 18?
–56
–52
52
56
Answers
Answer:
-52, I think
Step-by-step explanation:
find the slope of the tangent line to the polar curve =5 2θ at the point specified by the value θ=π/3.
Answers
Simplifying this expression will give you the slope of the tangent line to the polar curve at θ = π/3.
What is derivative?
The derivative provides information about the slope or steepness of a curve at various points and can be used to find critical points, determine the concavity of a function, and solve optimization problems. The derivative is denoted using various notations, such as f'(x), dy/dx, or df/dx, depending on the context and notation conventions.
To find the slope of the tangent line to the polar curve r = 5 + 2θ at the point specified by θ = π/3, we need to determine the derivative of the polar curve with respect to θ and evaluate it at θ = π/3.
The polar curve r = 5 + 2θ can be expressed in Cartesian coordinates as x = (5 + 2θ) * cos(θ) and y = (5 + 2θ) * sin(θ).
Now, let's find the derivative of y with respect to x using the chain rule:
dy/dx = (dy/dθ) / (dx/dθ)
To find dy/dθ and dx/dθ, we differentiate the expressions for y and x with respect to θ:
dy/dθ = d/dθ [(5 + 2θ) * sin(θ)] = (2 + 2θ) * sin(θ) + (5 + 2θ) * cos(θ)
dx/dθ = d/dθ [(5 + 2θ) * cos(θ)] = (2 + 2θ) * cos(θ) - (5 + 2θ) * sin(θ)
Now, we can calculate the derivative of y with respect to x:
dy/dx = [(2 + 2θ) * sin(θ) + (5 + 2θ) * cos(θ)] / [(2 + 2θ) * cos(θ) - (5 + 2θ) * sin(θ)]
To find the slope of the tangent line at θ = π/3, substitute θ = π/3 into the expression for dy/dx:
dy/dx = [(2 + 2(π/3)) * sin(π/3) + (5 + 2(π/3)) * cos(π/3)] / [(2 + 2(π/3)) * cos(π/3) - (5 + 2(π/3)) * sin(π/3)]
Simplifying this expression will give you the slope of the tangent line to the polar curve at θ = π/3.
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9/10 divided by 3/5
Answers
Answer:
1 1/2
Step-by-step explanation:
9/10 ÷ 3/5
Copy dot flip
9/10 * 5/3
Rewriting
9/3 * 5/10
3 * 1/2
3/2
1 1/2
Answer:
3/2
Step-by-step explanation:
9/10 ÷ 3/5
~Use copy dot flip
9/10 * 5/3
~Multiply
45/30
~Simplify
3/2
Best of Luck!
Let R represent the set of all real numbers.
Suppose f:R -> R has the rule f(x)=3x+2. Determine whether f is a function, injective, surjective and/or bijective. Choose all that apply.
A. Function B. Injective C. Surjective D. Bijective
Answers
Option D is the correct.
The given function f: R → R with the rule f(x) = 3x + 2. Let R represent the set of all real numbers.
What is a function?
A function is defined as the set of ordered pairs in which each first element of the ordered pair maps to one unique second element of the ordered pair.
What is an injective function?
A function f(x) is called one-to-one or an injective function, if and only if each and every element of the function domain is paired with exactly one element of the function range.
What is a surjective function?
A function f(x) is called onto or a surjective function, if and only if each and every element of the function range is paired with at least one element of the function domain.
What is a bijective function?
A function f(x) is called a bijection or a bijective function if it is both injective and surjective.
The given function is a function because for every x in R, there is exactly one image (3x+2) in R.
Let x₁, x₂ be two distinct real numbers in R, then3x₁ + 2 ≠ 3x₂ + 2, which implies f is injective or one-to-one.
Therefore, the given function f is both an injective function and a surjective function.
So, the function is a Bijective function
Option D is the correct choice. The given function f: R → R with the rule f(x) = 3x + 2 is Bijective function.
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whats the answer to the ixl 8th grade multiplying monomials question Simplify. Express your answer using positive exponents. 8d times 8d
Answers
The correct result regarding the multiplication of the monomials 8d and 8d is given as follows:
64d².
How to multiply monomials?Monomials are composed both by numeric coefficients and by algebraic variables, hence, to multiply them:
The numeric coefficients are multiplied.The algebraic variables are also multiplied, applying properties of exponents.In the context of this problem, the monomials that are multiplied are given as follows:
8d x 8d.
Hence the multiplication is obtained as follows:
The multiplication of the numeric coefficients is of 8 x 8 = 64.The multiplication of the algebraic variables is of d x d = d².For the variables, we applied the multiplication of two terms with the same base and different exponents, keeping the bases and adding the exponents.
Then the product is given as follows:
8d x 8d = 64d².
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Joey exercising everyday. Today he jogged for 8.40 minutes and sprinted for 0.65 minutes then jumped roped for 10.30 minutes and stretched for 5.25 minutes. Write a fraction to represent the total numbers of minutes that joey spent exercising
Answers
Answer:
286/20 or 14.3
Step-by-step explanation:
According to the Question,
Given, Joey exercising every day. Today he jogged for 8.40 minutes and sprinted for 0.65 minutes then jumped roped for 10.30 minutes and stretched for 5.25 minutes .jogged for 8.40 minutes = 8minute + 0.40minute ⇒ (8 + 4/10) ⇒ (8 + 2/5) Minutes.
sprinted for 0.65 minutes = 65/100 ⇒ (13/20)Minutes.stretched for 5.25 minutes = 5 + 25/100 ⇒ (5 + 1/4)Minutes.Total numbers of minutes that joey spent exercising = (5 + 1/4)Minutes + (13/20)Minutes. + (8 + 2/5) Minutes.⇒13 + 1/4 + 2/5 + 13/20
⇒13 + (5+2*4+13)/20
⇒13 + 26/20
⇒286/20 or 14.3 or 14 minutes 3/10 minute .
82% of 300 boys polled said that they liked to play outdoors. How many boys liked to play outdoors?
Answers
Answer:
246 boys like to play outdoors
Step-by-step explanation:
82% = 0.82
0.82 x 300 = 246
Answer:
246 boys like to play outdoors
Step-by-step explanation:
82% = 0.82
0.82 x 300 = 246
9. What is the slope of the graph of y= 12 x - 19?
Answers
12
Explanation:
Slope Intercept form is: y=mx+b
m would be the slope
So in y=12x-19, 12 would be the slope in this case.
Solve for x please help me
Answers
Answer:
It's C.
Step-by-step explanation:
12x+4+9x+8=180
Combine like terms 21x+12=180
Subtract 12 from both sides 21x=168
Divide each side by 21 21x/21=168/21
x=8
The dot plot above identifies the number of pets living with each of 20 families in an apartment building. What
fraction of the families have more than two pets?
Answers
Answer:
1/5
Step-by-step explanation:
is the square root parent function.
OA. F(x)=√x + 1
OB. F(x)=√x
O C. F(x) = x
OD. F(x) = x²
Answers
B. F(x)= √x
Calculate the iterated integral. (1 4xy) dx dy Step 1 When calculating e find the inner integral first. Since this is an integral with respect to x, then we consider x to be the variable and y to be a constant. Therefore, (1 + 4xy) dx dy
Answers
The first step of calculating the iterated integral involves finding the inner integral by integrating the integrand with respect to the variable x while considering y as a constant. This yields x + 2xy²
To calculate the iterated integral ∫∫(1 + 4xy) dxdy, we follow the process of integrating the inner integral first. In this case, x is treated as the variable while y is considered a constant.To find the inner integral, we integrate (1 + 4xy) with respect to x. Treating y as a constant, we obtain the integral ∫(1 + 4xy) dx. Integrating this expression yields x + 2xy² as the result.
Now, we have an expression for the inner integral: x + 2xy². The next step is to integrate this result with respect to y while considering the limits of integration for y. Without specific limits provided, we cannot determine the exact values for the integral. However, we can express the iterated integral in terms of the variable y, resulting in ∫(x + 2xy²) dy.
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Find the length of the apothem of a regular triangle with a perimeter of 96√3
units.
Answers
The length of the apothem of the regular triangle with a perimeter of 96√3 units is 16 units.
To find the length of the apothem of a regular triangle, we need to know the length of one of its sides. We are given the perimeter of the triangle, which is 96√3 units. Since a regular triangle has three equal sides, we can divide the perimeter by 3 to get the length of one side:
96√3 ÷ 3 = 32√3 units
Now, we can use the formula for the apothem of a regular triangle:
apothem = (side length) / (2 * tan(π/3))
where π/3 is the angle between the apothem and one side of the triangle (which is 60 degrees for a regular triangle).
Plugging in the values we have:
apothem = (32√3) / (2 * tan(π/3))
apothem = (32√3) / (2 * √3)
apothem = 16 units
Therefore, the length of the apothem of the regular triangle with a perimeter of 96√3 units is 16 units.
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