A Petri dish contains 100 bacteria cells. The number of cells increases 5% every minute. How long will it take for the number of cells in the dish to reach 2000? Use logarithms to solve.

Using logarithm, the following equation will apply:

Y = P * [1 + z]^x

Where Y = 2000

P = 100

z = 5% = 0.05

x is the quantity we are calculating for

The equation becomes

2000 = 100 * [1 + 0.05]^x

Dividing both side by 100, we have

20 = 10 * [ 1 + 0.05]^x

Taking the log of both sides, we have

Log 20 = Log [1 + 0.05]^x

log 20 = x * log 1.05

x = log 20 / log 1.05 = 61.40

Thus, it will takes 61.40 minutes for the number of cells in the petri dish to reach 2000.