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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

Respuesta :

Answer:

The answer is 14.46%

Step-by-step 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 = [tex]A=A0e^{rt}[/tex]

[tex]117360=20e^{r*60}[/tex]

[tex]5868=e^{60r}[/tex]

Taking log function (ln) on both sides.

[tex]ln(5868)=ln(e^{60r} )[/tex]

[tex]60r=8.677[/tex]

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

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