Question

A sample of bacteria experienced 5% daily growth compounded continuously for 14 days. At the end of the 14 days, the sample had reached a size of 80 bacteria. What was the sample size at the beginning of the 14 days? Round your answer up to the nearest whole number, and do not include units.

Answer 1

sample size at the beginning was 40 bacteria.

Explanation:

Given that a sample of bacteria experienced 5% daily growth compounded continuously for 14 days

Let C be the initial amount of bacteria.

C grows continuously compounding at the rate of 5%

The equation representing the number of bacteria at time t days would be

`P(t) = Ce^(0.05t)`

Now we have t = 14 days and P = 80.

Substitute to get

`80=Ce^(0.05(14)) \\C=80e^(-0.05(14))\\C=39.72682`

Approximately 40 bacteria were present at the beginning.