Question

The size S of a tumor in mm cubed is given by S=2^t, where t is the number of months since the tumor was discovered a: what is the total change in the size of the tumor during the first 6 months?
and b: what is the average rate of change in the size of the tumor during the first 6 months?
and c: estimate the rate at which the tumor is growing at t=6?

Answer 1

When t = 0, S = 2^0 = 1 
When t = 2, S = 2^2 = 4 
Change in size = 4 - 1 = 3 cubic mm. 

Average rate of change = (S(2) - S(0))/(2-0) = (4-1)/2 = 1.5 cubic mm/month