Question

There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.

Answer 1

p(t)=170 x (1.30)^t

Explanation:

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Answer 2

`P(t)=170\cdot (1.30)^t`

Explanation:

We have been given that there are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year.

We can see that deer population is increasing exponentially as each next year the population will be 30% more than last year.

Since we know that an exponential growth function is in form:
`f(x)=a*(1+r)^x`, where a= initial value, r=growth rate in decimal form.

It is given that a=170 and r=30%.

Let us convert our given growth rate in decimal form.

`30\text{ percent}=(30)/(100)=0.30`

Upon substituting our given values in exponential function form we will get,

`P(t)=170\cdot (1+0.30)^t`

`P(t)=170\cdot (1.30)^t`

Therefore, the function
`P(t)=170\cdot (1.30)^t` will give the deer population P(t) on the reservation t years from now.