The total bear population in a certain area is represented by the function P=120 (1.016) t, where t is time in years. How would you rewrite this equation to identify the weekly growth rate of the population? How would you solve this equation.

1) function: P = 120 (1.0160) ^t, t in years

2) weekly function

w = 52 * t = 52t

=> P (w) = 120 (1.016) ^ (52w)

3) growth rate = d P (w) / dw

d P (w) / dw = 120 * 52 * [ 1.016 ^ (52w) ] = 6240 [ (1.016) ^ (52w) ]

4) solution of the equation

Separate variables

d P (w) = [ 6240 (1.016) ^ (52w) ] dw

integrate from w = 0 until w

P (w) - Po = 7599.84 e ^ (0.82514w)

P (w) = Po + 7599.84 e ^ (0.82514w)