Question

A population of rabbits doubles every 60 days according to the formula P=10(2)^t/60, where P is the population of rabbis on day t. What is the value of t when the population is 320

Answer 1

Answer:

$320 = 10 (2)^{t/60}$

If we divide both sides by 10 we got:

$32 = 2^{t/60}$

We can apply natural log on both sides and we got:

$ln (32) = \frac{t}{60} ln(2)$

And solving the value of t we got:

$t = 60 \frac{ln(32)}{ln(2)}= 300$

So then we can conclude that after t = 300 days we will have approximately 320 rabbits  

Step-by-step explanation:

For this case we have the following function:

$P(t) = 10 (2)^{t/60}$

Where P is the population of rabbis on day t. And for this case we want to find the value of t when P =320 so we can set up the following equation:

$320 = 10 (2)^{t/60}$

If we divide both sides by 10 we got:

$32 = 2^{t/60}$

We can apply natural log on both sides and we got:

$ln (32) = \frac{t}{60} ln(2)$

And solving the value of t we got:

$t = 60 \frac{ln(32)}{ln(2)}= 300$

So then we can conclude that after t = 300 days we will have approximately 320 rabbits