Question

Let F(t) denote the increase in population in a city where t is in months, be given by:

F(t) = 4t² +5
where t = 0 denotes March 2010. Find the rate at which population was increasing in December
2010.

Answer 1

To find the rate at which population was increasing in December 2010, we need to find the value of F'(t) at t = 9 (December 2010 is 9 months after March 2010).

Taking the derivative of F(t), we get:

F'(t) = 8t

So, F'(9) = 8(9) = 72

Therefore, the rate at which population was increasing in December 2010 was 72 people per month.