Question

A colony of bacteria grows by 10% per hour. By what percent will the colony grow after five hours?

Answer 1

The colony will have grown by `color(green)(61.051%)` after `5` hours.

Explanation:

If `p_t` is the population of a colony after `t` time units and `r` is the growth factor per time unit:
`color(white)("XXX")p_t=p_0(1+r)^t`

For the given values
`color(white)("XXX")p_5=p_0(1+0.10)^5`
`color(white)("XXXX") = 1.1^5p_0`
`color(white)("XXXX")= 1.61051p_0` (calculator used here)
`color(white)("XXXX")=p_0+0.61051p_0`

`0.61051=61.051%`