Question

A bacteria culture starts with 120 and after 3 hours the population consists of 200 bacteria. What is the rate of the increase to the nearest percent?

Answer 1

This is a continuous compounded growth:

P = A . eⁿˣ, where A is the original value, P, the yielded value after a growth of 
"x" during a time = n ( n = time = 3 hours : given)

200 = 120(e)³ˣ

200/120 = (e)³ˣ

5/3 = (e)³ˣ

ln(5/3) = ln[(e)³ˣ

0.5108 = 3x.ln(e) (ln(e) = 1)

x = 0.5108/3 = 0.17
 so the HOURLY growth rate = 0.17

Answer 2

The rate of the increase to the nearest percent is 30 percent