Question

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1800 bacteria selected

from this population reached the size of 2025 bacteria in four hours. Find the hourly growth rate parameter.
Note: This is a continuous exponential growth model.
Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

PLEASE HELP ME I BEG YOU

Answer 1

x = .0821 or 8.21%

Explanation:

Plug information into Pe^(rt)

1800e^(4t) = 2025

Isolate e

(1800e^(4t) = 2025)/1800

e^(4x) = 2500/1800

Use ln to cancel e

ln(e^4x) = ln(2500/1800)

4x = ln(2500/1800)

Isolate x

(4x = ln(2500/1800))/4

x = (ln(2500/1800))/4

Plug into calculator

x = .0821