A population of bears increased by 50% in 4 years.

Question

If the situation is modeled by an annual growth rate compounded continuously, which formula could be used to find the annual rate according to the exponential growth function? Leave your answer in terms of ln.

Answer 1

P(t) = C*exp(kt)

P0 = C*exp(k*0) = C*1 = C <--- initial population is P0

P1 = P0*exp(k*1) = P0 * exp(k)

P2 = P0*exp(2k)

P3 = P0*exp(3k)

P4 = P0 * exp(4k) = 1.5*P0 <--- population increases by 50% after 4 years

exp(4k) = 1.5

4k = ln(1.5)

k = ln(1.5)/4