Question

The current circulation of a particular magazine is 3,000 copies per week. The editor projects a growth rate of

g(t) = 4 + 5t^2/3

copies per week after t weeks.

a. Find the circulation function based on this projection.

b. Find the circulation in 2 years.

Answer 1

Let C(x) be the circulation function
given: C ' (x) = 4+5t^(2/3)
then
C(x) = 4t + 3t^(5/3) + c, where c is a constant
when x = 0 (now) , C(0) = 3000
3000 = 0 + 0 +c

so C(x) = 4t + 3t^(5/3) + 3000

so in 2 years, x = 2
C(2) = 8 + 3(2)^(5/3) + 3000
= appr 3018