Im having trouble getting the correct answer to this question. Could someone help out.

Question

Monthly sales of a particular personal computer are expected to decline at the following rate of S'(t) computers per month, where t is time in months and S(t) is the number of computers sold each month.

S'(t)= -15t^2/3

The company plans to stop manufacturing this computer when monthly sales reach 600 computers. If monthly sales now (t=0) are 1140 computers,find S(t). How long will the company continue to manufacture this computer.

Answer 1

1140 - 15t^(2/3) = 600,
-15t^(2/3) = 600 - 1140 = - 540,
Divide both sides by -15:
t^(2/3) = 36,
Take log of both sides:
2/3logt = log36,
Multiply both sides by 3/2:
logt = 3/2log36,
logt = 2.3345,
t = 10^(2.3345) = 216 months.