I need some help.

Question

A biologist finds that the population of a certian type of bacteria double seach half-hour. An initial culture has 60 bacteria.

1. What is the population after 3 hours?

2. How long will it take for the number of bacteria to reach 983,040?

Answer 1

let number = 60 (2)^(2t) , where t is in hours

when t = 3
number = 60 (2)^6 = 3840

2. we would be solving
60 (2)^(2t) = 983040
2^(2t) = 16384 which just happens to be 2^14

so 2^2t = 2^14
2t = 14
t = 7 , it would take 7 years

it was probably a planned question, if not we would have had to use logarithms