After years of overhunting, environmental scientists have reintroduced bears to Yellowstone National Park. The initial number of bears reintroduced to the park was 20 and, after 10 years, the population is estimated to be around 110.

Part A: Assuming an exponential growth pattern, use the information given to write the model for this situation.

Question

After years of overhunting, environmental scientists have reintroduced bears to Yellowstone National Park. The initial number of bears reintroduced to the park was 20 and, after 10 years, the population is estimated to be around 110.

Part A: Assuming an exponential growth pattern, use the information given to write the model for this situation.

aveline · Answer

Let's use $$y=A(1+r)^ {t}$$
where A represents the initial population, r represents the rate of growth, t represents the time interval, and A represents the total population.

The initial number, A, is 20.
The time interval, t, is 10 years.
The total population, y, is 110.

So now we can fill in the equation:

$$110=20(1+r)^ {10}$$

kiki99 · Answer

okay thanks i was just about to put my result in and ask if it was right

kiki99 · Answer

can you help me with part B? @Aveline

kiki99 · Answer

What is the annual growth rate (rounded to the nearest tenth of a percent) of the new bear population in Yellowstone National Park?

aveline · Answer

Yeah.

aveline · Answer

We have our equation $$110=20(1+r) ^{10}$$
First, we divide 20 from each side:
$$5.5=(1+r)^ {10}$$
Can you simplify from here?

kiki99 · Answer

5.5/20=110

kiki99 · Answer

what do i do to the other side what do i divide by 20

aveline · Answer

I already divided 20 for you ;)

kiki99 · Answer

oh okay no we could not simplify any further

kiki99 · Answer

is that it? @Aveline

aveline · Answer

You need to simplify the exponents.

kiki99 · Answer

@Aveline i dont remember how