I need help with this multivarible calculus problem Assume that the population d

Question

I need help with this multivarible calculus problem

Assume that the population density P (in people/square kilometer) of a city can be modelled as a function of the distance R (in kilometers) from the city center and the number of years t since 1950. Thus P(R, t) when R = 5km and t = 10 for example, represents the population density 5km from the city center in the year 1960. Match the following quantities to the partial derivatives they approximate and give the units of each: P_R (10, 20) P_r (10, 20) P_RR (10, 20) P_Rt(10, 20) P_tt(10, 20) P_tR(10, 20)

Explanation / Answer

The first one is the average rate of change of partial derivative of P with time with respect to distance R, keeping time constant at t = 20

This is given by option D

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The second one is the average rate of change of partial derivative of P with distance R with respect to distance R keeping time cinstant at t = 20

This is given by option C

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