The number of children under 18 living in households headed by a grandparent can be modeled as p(t) 2.111e.04t million children where t is the number of years since 1980.t (a) Write the rate-of-change formula for p. P'(t) 0.084e0.04r million children per year (b) How rapidly was the number of children living with their grandparents growing in 2002? (Round your answer to three decimal places.) Xmillion children per year 0.203

Question
The number of children under 18 living in households headed by a grandparent can be modeled as
p(t) 2.111e.04t million children
where t is the number of years since 1980.t
(a) Write the rate-of-change formula for p.
P'(t) 0.084e0.04r
million children per year
(b) How rapidly was the number of children living with their grandparents growing in 2002? (Round your answer to three decimal places.)
Xmillion children per year
0.203
Expand
Transcribed Image Text

The number of children under 18 living in households headed by a grandparent can be modeled as p(t) 2.111e.04t million children where t is the number of years since 1980.t (a) Write the rate-of-change formula for p. P'(t) 0.084e0.04r million children per year (b) How rapidly was the number of children living with their grandparents growing in 2002? (Round your answer to three decimal places.) Xmillion children per year 0.203

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Derivative

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: What are the coordinates used to evaluate the following problem and how are they found?

A: Given that D is a region that lies below the sphere and above a cone.

Q: Calculus Question

A: Dividing by highest denominator power ie by x 

Q: 2. If you graph the function 1 - el/ x f(x) 1+el/x you will see that f appears to be an odd function...

A: Recall the following fact.

Q: find the absolute extrema for f(x) = x^2/3 (2-x) on [-1,2]   I know the critical points are 4/5 and ...

A: compute the critical points as follows.

Q: Can you help me step by step?

A: Click to see the answer

Q: 1. Find the following limits. e3r lim 3.x е (a) (b) lim e3/(2-a) lim In(1x2 - In(1 x (c) _ (d) lim l...

A: Click to see the answer

Q: F(x)=4+54x-2x^3 , [0,4]  what are the absolute minimum value and absolute maximum values?

A: Given function

Q: find the critical points, points of inflection, local maxima and minima and graph the function:

A: Given,

Q: How do you find the spherical coordinates of the following problem?

A: Given, Triple integral is

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) e9x e~x (a) Find the int...

A: NOTE: As you have posted a question with multiple subparts, we will answer the first subpart as per ...

Q: Need help and exlination on solving this problem

A: Click to see the answer

Q: Can you help with this problem step by step?

A: The problem is concerned with the critical points (maximum, minimum) of the given graph

Q: Can you help with this problem step by step?

A: (a) Finding the local extremas:

Q: I need help with question 15 in Section 3.11, page 264, of the James Stewart Calculus Eighth Edition...

A: Using the identity

Q: -32-9 9-4 2. Consider the following function f: r2 r< 1 f (x) = Find lim,1-f (x) (a) (b) Find lim,1+...

A: The given function is,

Q: Finding derivative.

A: Given,

Q: Iodine 131 is a radioactive material that decays according to the function A(t)=A0e-0.087(t) where A...

A: Refer to the question . we have been given the iodine 131 which is a radioactive material that decay...

Q: Starting with the graph of f(x) = 6*, write the equation of the graph that results from (a) shifting...

A: (a)

Q: Can you do question 21 and show the steps

A: the equation of line.

Q: Express the given quantity as a single logarithm In(x 2)7 In x In(x23x 2)2 2

A: Click to see the answer

Q: Homework help: Question: A ball is thrown vertically upward from the ground at a velocity of 98 feet...

A: compute the velocity function by differentiating the given function.

Q: Let f(x,y)= 3+cos(x) sin(2y) a) Show that the function has a stationary point at (0,Pi/4). b) Is (0,...

A: To analyze the critical point (0,pi/4) of the given function of two variables

Q: When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past...

A: Differentiate F with respect to R to get 

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: I need help working this problem. I get stuck at this point. I think my algebra is failing with the ...

A: Given function: m(t)=2/(t-1)

Q: For the given function, find all values of cover the interval (4, 8) stipulated by Rolle's Theorem s...

A: Given function in interval (4, 8)

Q: Can you help with this problem step by step?

A: Given function is

Q: For the composite function, identify an inside function and an outside function and write the deriva...

A: Given function

Q: Use the Quotient Rule to differentiate the function f(x) = (tan(x) − 1)/(sec(x)   Simplify the expre...

A: Given:

Q: Solve. (4^x)^2-2(4^x)-1=0

A: Click to see the answer

Q: A cylindrical drill with radius 2 is used to bore a hole through the center of a sphere of radius 6....

A: This can be solved with Cylindrical Shells.With radius = x, from 2 to 5.And height = 2y , where y= s...

Q: Use the limit process to find the area of the region between the graph of the function and the x-axi...

A: Given:Use the limit process to find the area of the region between the graph of the function and the...

Q: find any x-values where the tangent to the curve is horizontal, where y=x^3-6x^2+9x+1

A: The given equation of curve is,

Q: 2. Describe each of the following with a parametrization. Be sure to indicate the possible values fo...

A: To determine:Part a) The parametric equation of circle.Part b) Parametric equation of a point.

Q: Can you help with this problem step by step?

A: given function is

Q: Can you help with this problem step by step?

A: Given function is

Q: check my answer 5x+3y=-6 x=3 2x-3y=27 y=-7

A: Given system of equations are 

Q: Find positive numbers x and y satisfying the equation xy=15 such that the sum 3x+y is as small as po...

A: Click to see the answer

Q: Can you help with this problem step by step?

A: Given function

Q: dt = (c) (9+t2)3/2

A: Given:

Q: Find the derivative of

A: Given,