Question

The number of bacteria in a culture increases continuously and rapidly when put under a heat source. a culture containing 20 bacteria multiplies to 117,360 in one minute.

a.what is the rate of increase, as a percentage to the nearest hundredth, if time is measured in seconds

Answer 1

The answer is 14.46%

Explanation:

Given is : A culture containing 20 bacteria multiplies to 117,360 in one minute.

Let A0 be initial bacteria count = 20

Let A be final bacteria count = 117360

Time = 60 seconds

R = rate

Formula to be used =
`A=A0e^(rt)`

`117360=20e^(r*60)`

`5868=e^(60r)`

Taking log function (ln) on both sides.

`ln(5868)=ln(e^(60r) )`

`60r=8.677`

Hence, r = 0.1446 and in percentage it is 14.46%