rate of change?

Question

because of lack of promotion, the yearly sales S of a product decline according to the equation S(t)=3000e^-0.80t where t is the time.

Find:
a. the rate of change of sales with respect to time.
b. the rate of change of sales at t=0.5
c. the rate of change of sales at t=2

Answer 1

Rate of chage is derivative with respect to time

dS/dt = 3000*(-0.8)e^(-0.8*t) = -2400*e^(-0.8*t)

b. At t = 0.5 dS/dt = -2400 *e^(-0.8*0.5) = 1608.7

c. t = 2 dS/dt = 484.5

Answer 2

dS/dt = -.8*3000e^-.8t = 2400e^-.8t
2400 e^-(.8*.5) = 1608.77=rate of change at t = .5
2400 e^-(.8*2) = 484.55 =rate of change at t = 2