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

The answer is: 10.90 hours

Explanation:
Please see the image attached!

Answer 2

It takes 10.9 hours.

We set the equation equal to 1792000:

$1792000=3600(2)^{\frac{t}{73}}$

Divide both sides by 3600:
$\frac{1792000}{3600}=\frac{3600(2)^{\frac{t}{73}}}{3600} \\ \\\frac{4480}{9}=2^{\frac{t}{73}}$

We will use logarithms to solve this:
$\log_2{\frac{4480}{9}}=\frac{t}{73}$

Multiply both sides by 73:
$73\log_2{\frac{4480}{9}}=t \\ \\654.03=t$

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