Question

A microbiologist determines that a colony of bacteria doubles every hour. If at the start (t = 0) there are 10 in the colony, a) What is the population at the end of 1 day? b) Write an equation to give the population at any given hour.

c) When will the population exceed 100,000?

Answer 1

Explanation:

Exponential formula

n = 10 (2)^x

x is the number of hours n is the number of bacteria in the colony

After ONE day....x = 24 (hours)

n = 10* 2^24 = 176 772 160

100 000 < 10 * 2^x solve for 'x'

10000 < 2^x log both sides

log 10000 < x log 2

log 10000 / log 2 < x

x > 13.287712 hr <====== (ROUND AS NECESSARY)