Pre-Calc AB P=1500/1+8e^0.15t

Question

A wildlife organization released a group of animals that are an endangered species into a preserve. The equation below models the population, P, of the species t months after the initial release. What will be the population of this endangered species in the preserve after 1 year?

P = 1500/1+8e^0.15t

Answer 1

Hi Kit!

Let's take a look at the question:

A wildlife organization released a group of animals that are an endangered species into a preserve. The equation below models the population, P, of the species t months after the initial release. What will be the population of this endangered species in the preserve after 1 year?

P=1500/(1+8e^0.15t)

Now, I am going to write out what each variable represents:

P=Population after initial release

t=number of months after initial release.

It is important to remember that e is not a variable as it represents a single number.

They are asking for the population (P) after 1 year. We know that 1 year =12 months, so what we are going to do is plug it into the t value in the equation:

P=1500/(1+8e^{0.15 x 12})

P=1500/(1+8e^1.8)

P=1500/49.397179

P=30.366

However, P must be a whole number, as we are counting the number of animals-half an animal would not be a good thing! So, we will round down to 30.

The population will be 30 animals.