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.

The Answer is approximately 12.71 seconds.

Step-by-step 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