For Exercises 1–3 , do the following. Graph the reproduction curve, the line y = P , and the harvest function using the same viewing window. Find the population at which the maximum sustainable harvest occurs. Use both a graphical solution and a calculus solution. Find the maximum sustainable harvest. f ( P ) = − 0.01 P 2 + 2 P , where P is measured in thousands. This is the reproduction curve in the Hudson Bay area for the lynx.
For Exercises 1–3 , do the following. Graph the reproduction curve, the line y = P , and the harvest function using the same viewing window. Find the population at which the maximum sustainable harvest occurs. Use both a graphical solution and a calculus solution. Find the maximum sustainable harvest. f ( P ) = − 0.01 P 2 + 2 P , where P is measured in thousands. This is the reproduction curve in the Hudson Bay area for the lynx.
Solution Summary: The author explains how to graph the reproduction curve of the function f(P)=-0.01 P2+2P and the harvest function.
Insurance Rates The following table gives themonthly insurance rates for a $100,000 life insurancepolicy for smokers 35–50 years of age.a. Create a scatter plot for the data.b. Does it appear that a quadratic function can beused to model the data? If so, find the best-fittingquadratic model.c. Find the power model that is the best fit for the data.d. Compare the two models by graphing each modelon the same axes with the data points. Whichmodel appears to be the better fit?
World Military Expenditure The following chart shows total military and arms trade expenditure from 2011–2020 (t = 1 represents 2011).
†A bar graph titled "World military expenditure" has a horizontal t-axis labeled "Year since 2010" and a vertical axis labeled "$ (billions)". The bar graph has 10 bars. Each bar is associated with a label and an approximate value as listed below.
1: 1,800 billion dollars
2: 1,775 billion dollars
3: 1,750 billion dollars
4: 1,730 billion dollars
5: 1,760 billion dollars
6: 1,760 billion dollars
7: 1,850 billion dollars
8: 1,900 billion dollars
9: 1,950 billion dollars
10: 1,980 billion dollars
(a)
If you want to model the expenditure figures with a function of the form
f(t) = at2 + bt + c,
would you expect the coefficient a to be positive or negative? Why? HINT [See "Features of a Parabola" in this section.]
We would expect the coefficient to be positive because the curve is concave up.
We would expect the coefficient to be negative because the…
Use this information to solve Exercises 9–11:A company is
planning to produce and sell a new line of computers. The fixed
cost will be $360,000 and it will cost $850 to produce each
computer. Each computer will be sold for $1150.
9. Write the cost function, C, of producing x computers.
10. Write the revenue function, R, from the sale of
x computers.
11. Determine the break-even point. Describe what this
means.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.