Your monthly car payment in dollars is P = f(Po,t, r), where $Po is the amount you borrowed, t is the number of months it takes to pay off the loan, and r percent is the interest rate. (a) Is OP/at positive or negative? negative v Suppose that your bank tells you that the magnitude of aP/dt is 35. What are the units of this value? (For this problem, write our your units in full, writing dollars for S, months for months, percent for %, etc. Note that fractional units generally have a plural numerator and singular denominator.) (b) Is aP/Or positive or negative? positive Suppose that your bank tells you that the magnitude of aP/ar is 5. What are the units of this value? (For this problem, write our your units in full, writing dollars for $, months for months, percent for %, etc. Note that fractional units generally have a plural numerator and singular denominator.) For both parts of this problem, be sure you can explain what the practical meanings of the partial derivatives are.

þne statement of Boyle's law is that the pressure of a gas varies inversely as the volume for constant temperature. If a certain gas occupies 670 cm when the pressure is 260 kPa and the volume is increasing at the rate of 20.0 cm /min, how fast is the pressure changing when the volume is 800 cm? .... Boyle's law indicates that the pressure of a gas, P, varies inversely as the volume, V, for constant temperature, C. Write an equation for P with respect to V and C. P= V when the volume is 800 cm The pressure is changing at a rate of (Type an integer or decimal rounded to one decimal place as needed.)

Find the consumers' surplus (to the nearest dollar) at a price level of p = $2.083 for the price-demand equation p = D(x) = 9 - In (x+ 6). Use x computed to the nearest higher unit. Cs = $ (Simplify your answer. Round to the nearest dollar as needed.)

The table below gives the population of the small (imaginary) town of Wisteria. What is the average rate of change of the town's population from 1970 to 1980? Give your answer with one decimal place of accuracy to the right of the decimal point, and give appropriate units for your answer.