Question

The population P of a colony of 3600 bacteria at time t minutes can be modeled by the function P(x) = 3600(2)^t/73. How long does it take the population (in hours) to reach 1,792,000?

Answer 1

It takes 10.9 hours.

We set the equation equal to 1792000:


`1792000=3600(2)^{(t)/(73)}`

Divide both sides by 3600:

`(1792000)/(3600)=\frac{3600(2)^{(t)/(73)}}{3600} \\ \\(4480)/(9)=2^{(t)/(73)}`

We will use logarithms to solve this:

`\log_2{(4480)/(9)}=(t)/(73)`

Multiply both sides by 73:

`73\log_2{(4480)/(9)}=t \\ \\654.03=t`

This is in minutes; to convert to hours, divide by 60:
654.03/60 = 10.9

Answer 2

The answer is: 10.90 hours

Step-by-step explanation:
Please see the image attached!