Question

A population of bacteria is growing at the rate of 2.3% per minute. How long will it take for the size of the population to double? Give your answer to the nearest minute.

Answer 1

Present Population = Starting Population * (1.023)^minutes
So, we need to know when Present Population = Starting Population *2

Present Population = Starting Population * (1.023)^minutes
Taking logs of both sides
log(Pres) = minutes * log(Start*1.023)
Let's say Start = 1
log(Pres) = minutes * log(1*1.023)
log(Pres) = minutes * 0.0098756337
log(Pres) / .0098756337 = minutes

We need to know when Pres = 2
log(2) / .0098756337 = minutes

0.3010299957 / .0098756337 = minutes

= 30.4820940547 minutes

Answer 2

Double Check
Present Population = Starting Population * (1.023)^minutes
We need to know when pres ent population =2

2 = 1 * (1.023)^30.4820940547

(1.023)^30.4820940547 does equal 2 so

30.4820940547 minutes is the answer OR the answer to the nearest minute is
30 minutes.