Question

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.

Answer 1

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)

Answer 2

Answer:

r= .016*100=1.6

R= 1.6%

R=1.6 over 52*100= 0.03076923077 per week

Growth= 0.03

function= P=120(1.016^1/52)^52t

Hope this helps! ^-^