Positive Exponent

Question

A bacteria culture is started with 200 bacteria. After 4 hours, the population has grown to 773 bacteria. If the population grows exponentially according to the formula (a) Find the growth rate. Round your answer to the nearest tenth of a percent.

Answer 1

P(t)=P₀(1+r)^t

773=200(1+r)⁴

1+r = (773/200)^0.25

r = 1.402-1 = 0.402 = 40.2%

Answer 2

773 = 200(1 + r)⁴

773/200 = (1 + r)⁴

(773/200)^1/4 = 1 + r

r = (773/200)^1/4 - 1

r = 0.4 = 40%