The growth of a certain strain of bacteria is given by the e

The growth of a certain strain of bacteria is given by the equation C = I(2.4)^0.621t, where C is the final number of bacteria, I is the initial number of bacteria, and t is the number of hours. If the initial number of bacteria was 7, find the numbers of hours required for the colony to reach 3200 bacteria. Round the answer to the nearest tenth of an hour]

Solution

Given relation is

C = I*(2.4)^0.621*t

Where each term has its usual meaning.

Here C = 3200

I = 7

Then

3200 = 7*(2.4)^0.621*t

(2.4)^0.621*t = 457.14

0.621*t*ln2.4 = ln(457.14)

t = 11.3 hrs