Question

There are 170170170 deer on a reservation. The deer population is increasing at a rate of 30\%30%30, percent per year. Write a function that gives the deer population P(t)P(t)P, left parenthesis, t, right parenthesis on the reservation ttt years from now. P(t)=P(t)=P, left parenthesis, t, right parenthesis, equals

Answer 1

Answer:

$P(t)=170X1.3^{t-1}$

Step-by-step explanation:

• There are 170 deer on the reservation.

• The deer population is increasing at a rate of 30% percent per year.  

If the deer population increases at a rate of 30% each year, this increase is a ratio.

Any sequence in which the next term is gotten from the previous term by multiplication by a constant ratio is a geometric sequence.

If the Initial Population P(1)=170

The next population, P(2)= 170+(30% of 170)= 130% 0f 170

Clearly, our constant/common ratio=130%=1.3

The nth term of a geometric sequence is given as $U_{n}=ar^{n-1}$

Where a= first term, r=common ratio, n=number of terms.

P(1)=a=170,

r=1.3

Therefore:

$P(t)=170X1.3^{t-1}$ where t is the number of years.

Answer 2

Answer:

170 x 1.3^t

Step-by-step explanation:

the answer above is correct, but its not ^t-1, its just ^t