Question

@campbell_st one last question:)
Suppose that the demand function for a product is given by D(p)=35000/p and that the price p is a function fo time given by p=1.5t+10, where t is in days.
a) find the demand as a function of time t
b) find the rate of change of the quantity demanded when t=100

I know a) 35000/(1.5t+10)
but b? Do I find the deriv then input t=100?

Answer 1

substitute p = 1.5t +10 into the demand function

then find 1st derivative using the chain rule

rewrite the demand function in index form

\[D = 3500(1.5t +10)^{-1}\]

Answer 2

So -2.05078?