How quickly was the population changing at the start of 1985?

Question

The number of rabbits in a forest varies with time. During the period of 1980 to 1990 the number is given approximately by the formula 8000+5000sin(2πt/5) where t is the number of years after 1980.

 

How quickly was the population changing at the start of 1985?

 

I keep getting this last part of the question wrong! I thought it'd be 40,000 but thats wrong. 

Answer 1

Given x=8000+5000*sin(2/5*pi*t). dx/dt = 5000*2/5*pi*cos(2/5*pi*t). At t=5, dx/dt(5)=2000*pi*cos(2/5*5*pi)

= 2000*pi*cos(2*pi)=6283.185307... This is the largest possible answer.