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After years of overhunting, environmental scientists have reintroduced mountain goats into Yellowstone National Park. The initial number of mountain goats reintroduced to the park was
1,500; after 11 years, the population
is estimated to be around 8,400. Assuming an exponential growth pattern, what is the annual growth rate (rounded to the nearest tenth of a percent) of
the new mountain goat population in Yellowstone National Park?
Hint: All) = Ao(t +)', where Aft) is the final amount, Ao is the initial amount,r is the growth rate expressed as a decimal, and t is time.

a.) 0.17%

b.) 1.7%

c.) 17.0%

d.) 17.9%

Sagot :

facundo3141592

We want to see how much the population of goats grows each year. We will see that the correct option is c: 17%.

Exponential growth of populations

We know that:

  • The initial number of goats is 1,500.
  • After 11 years, the population is 8,400.

The population can be modeled with an exponential equation as:

P(t) = A*(1 + r)^t

Where:

  • A is the initial population.
  • r is what we want to find, it depends on how much the population increases.
  • t is the time in years.

So we have:

P(t) = 1500*(1 + r)^t

And we know that after 11 years the population is 8,400, so we have:

P(11) = 1500*(1 + r)^11 = 8400

Now we can solve this for r:

(1 + r)^11 = 8400/1500 = 5.6

(1 + r) = (5.6)^(1/11) = 1.17

r = 1.17 - 1 = 0.17

r = 0.17

To get it in percentage form, you just need to multiply it by 100%

0.17*100% = 17%

This means that the population increases a 17% each year, so the correct option is c.

If you want to learn more about exponential growth, you can read:

https://brainly.com/question/13223520

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