Math

CalculusQ&A LibraryThe population (in millions) of the United States between 1970 and 2010 can be modeled as p(x) = 203.12e0.011x million people where x is the number of decades after 1970.The percentage of people in the United States who live in the Midwest between 1970 and 2010 can be modeled as m(x) = 0.002x2 − 0.213x + 27.84 percent where x is the number of decades since 1970.† How rapidly was the population of the Midwest changing in 1980 and in 2010? (Round your answers to three decimal places.) 1980 million people per decade 2010 million people per decadeStart your trial now! First week only $4.99!*arrow_forward*

Question

The population (in millions) of the United States between 1970 and 2010 can be modeled as

p(x) = 203.12e^{0.011x} million people

where *x* is the number of decades after 1970.

The percentage of people in the United States who live in the Midwest between 1970 and 2010 can be modeled as

m(x) = 0.002x^{2} − 0.213x + 27.84 percent

where *x* is the number of decades since 1970.†

How rapidly was the population of the Midwest changing in 1980 and in 2010? (Round your answers to three decimal places.)

1980 | million people per decade | |

2010 | million people per decade |

Tagged in

Math

Calculus

Find answers to questions asked by students like you.

Q: dx Evaluate 256 289x2 dx 256-289x (Use C as an arbitrary constant.)

A: Substitute for x as follows.

Q: Find the absolute extrema of the function on the interval [2, 3]. (Round your answers to the nearest...

A: compute the critical points as follows.

Q: Find the limit as x approaches infinity of f(x) when f(x) is x times square root of x

A: x times sqrt(x)= x times x^(1/2)= x^[1+1/2] = x^(3/2)

Q: indeterminate forms?

A: Indeterminate form is an expression involving functions whose limit cannot be determined from the li...

Q: The initial size of a particular substance is 75. After 3 hours the substance count is 4500. 6. Find...

A: We are given that the initial size of a particular substance is 75 and after 3 hours the substance c...

Q: Let f (x) = x1/3(8x + 12)2/3. Find f ' (x) and the critical numbers for f.f ' (x) = (Ax+B)/3x^c(8x...

A: Use product rule to find the derivative. Use chain rule for (8x+12).

Q: Use integration by parts to evaluate the integral. ∫0π/3 5exsinx dx type an exact answer

A: Given, definite integration is

Q: 1 Q 2. Differentiate h(x) = (V+ -2 IX

A: The equation can be re written as,

Q: Let f(x,y)= x2-y2 a) On the set of xy-axes, draw the level curves L(x,y) = k for k= 1,2,3. On anothe...

A: The level curves f (x, y) = k are just the traces of the graph of f in the horizontal plane z = k pr...

Q: For the demand equation, use implicit differentiation to find dp/dx. 17p2 + 5p + 6 = x

A: Given:

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

A: You have asked two unrelated questions in the same post. I will address all the sub parts of the fi...

Q: please answer the question provided in the images with this function: h(x)=(5x^3) - (3x^5)

A: Since your question has multiple sub parts, we will answer the first three sub parts of your questio...

Q: For the given cost function C(x)=28900+500x+x2 find:a) The marginal cost at the production level 135...

A: The marginal cost at the production level 1350 is C'(1350)Answer(a): 3200

Q: Differential Equestion

A: You have asked a question with multiple sub parts. I will address the first three of them. Please po...

Q: Find the derivative.

A: Click to see the answer

Q: Make an appropriate substitution and then use integration by parts to evaluate the integral. dx e

A: Click to see the answer

Q: see attachment

A: The relation between the temperature and the height above a distance planet is,

Q: Angle of tangent to curve 8 of 13 Review Constants Part A What angle does the tangent to the curve y...

A: Click to see the answer

Q: For children between the ages of 5 and 13 years, the Ehrenberg equation ln W = ln 2.4 + 1.84h gives ...

A: Given data;

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

A: Make the coefficients into exponent. And they will multiply with the existing exponents.

Q: find the derivative 1).f(x)=X^3(X^4/3-1) ...

A: 1)

Q: I am very confused about this chapter and specifically on how the homework is breaking the problems ...

A: Given sequence is

Q: This is a 2 part question, kind of.... Part 1: Find the derivative.f (t) = 3t sin2 t Part 2: Is ther...

A: Given function is:Applying the derivative with respect to t and using the chain rule i.e. (uv)' = u'...

Q: As the limit apporaches infinity, find the limit of (8sinx+7cosx)/(x).

A: Given limit function

Q: 10 5 0 -1 -10 Identify the graphs A (blue), B( red) and C (green) as the graphs of a function and it...

A: A(blue) is the graph of the functionB(red) is the graph of the function's first derivativeC(green) i...

Q: The half-life of iodine-123 is about 13 hours. You begin with 52 grams of iodine-123. (a) Write an...

A: Consider the amount of iodine(I) as a function of time(t).

Q: Find a polynomial function with real coefficients that has the given zeros. (There are many correct ...

A: Given that the polynomial with real coefficients has a complex zero 9i. then by complex conjugate th...

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

A: Click to see the answer

Q: Find the derivative using the following information.

A: Equation of tangent to curve g(x) at x=2 is y=-3x+2. Its slope is m=-3. Since slope of tangent to cu...

Q: Match the blue graph of each function to the black graph of its derivative by writing the letter (A,...

A: Consider the first function:

Q: While taking a walk along the road where you live, you accidentally drop your glove, but you don't k...

A: That you dropped it within 1 kilometer of home this means 0≤x≤1We have to find the probability P(0≤x...

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

A: Given,

Q: Finding derivative.

A: Given function can be expressed as

Q: Why is f(0)=2 not included as an answer?

A: f(0)=2 is an end point. Because the domain is [0,7)So values on the left side of x=0 does not exist....

Q: Find the derivative of y with respect to x. y= csc^-1 (x^2+1) , x>0

A: Given ,

Q: if sin(0)=-7/25 with 0 quadrant IV, what is cos(0)?

A: Given

Q: Francisco's gross income this year is $29,550. His employer withholds $55 per month to pay for his ...

A: Francisco’s gross income = $29,550 in a yearEmployer withhold = $55 per month and employer withhold ...

Q: I need help with question 23 in Section 3.9, page 250, of the James Stewart Calculus Eighth Edition ...

A: In order to calculate the rate of change in the distance between the ships at 4.00 pm, use the given...

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

A: Given surface equation is

Q: A right triangle has side lengths 8, 15, and 17 as shown below. Use these lengths to find tan B, sin...

A: To determine the basic trigonometric ratios of the given angles

Q: see attachment

A: To determine the value of x.

Q: Find the point "P" on the graph of the function y=sqrtx closest to the point (10,0) The x coordinat...

A: Let the point is (x,y)= (x,sqrt(x))Distance of (x,sqrt(x)) from (0,0) is D

Q: A voltage V across a resistance R generates a current I=V/R. If a contant voltage of 6 volts is put ...

A: Click to see the answer

Q: see attachment

A: So the vector w is

Q: Sketch the graph of a function that satisfies the following 3. conditions: (a) f'(0) f'(2) = f'(4) =...

A: There are many ways to draw the graph. From part (a), observed that the function has local minimum o...

Q: Name: Gisselle Washington Optimization problems Date: Oct. 23, z01q Period: 1 Prove Show that of all...

A: Let length and breadth of the rectangle is x and y respectively.

Q: Find the area of the largest rectangle that can be inscribed in an equilateral triangle of side leng...

A: Given: A rectangle inscribed in an equilateral triangle of side L assuming one side of the rectangle...

Q: 0 and f" (x) < 0 for all x 50. Suppose f(3) = 2, f'(3) and f'(x) 2 a. Sketch a possible graph for f ...

A: We can conclude from f(3) = 2 that the value of f(x) at x = 3 is 2.So we got one point on the curve ...

Q: 1. Consider the function p(x) = C/1- x2 defined on [-1, 1] (a) Find a value C such that p(x) is a pr...

A: (a) The value of C is evaluated as follows.