Question

How many hours will it take a culture of bacteria to increase from 20 to 2,000 if the growth rate per hour is 85%?

Answer 1

Approximately `color(green)(7.5 " hours")`

Explanation:

We are trying to determine the value of `color(blue)(h)` in the compound growth formula
`color(white)("XXX")20xx(1+0.85)^color(blue)(h) = 2000`
or, simplified:
`color(white)("XXX")1.85^color(blue)(h)=100`

Taking the `log_(1.85)` of both sides:
`color(white)("XXX")log_(1.85) 100`

With the aid of my trusty spreadsheet:
`color(white)("XXX")h~~7.48582192`