Question

The mass of bacteria in a labaratory experiment increases exponentially by 22% each hour. The mass of bacteria was 8 micrograms when the experiment began. You are interested in predicting how long it will take for the mass of bacteria to reach 100 micrograms.

Answer 1

The Answer is approximately 12.71 seconds.

Explanation:

The form of the equation is:

f(x) = ab^x

Substitute:

f(x) = 8(1.22)^x

Solve for:

f(x) = 100

100 = 8(1.22)^x

100/8 = 1.22^x

12.5 = 1.22^x

1.22^x = 12.5

log(1.22^x) = log(12.5)

x * log(1.22) = log(12.5)

x * 0.0863 = 1.0969

x = 1.0969 / .0863 = 12.71 seconds, approximately