In 2016 a population of deer in an area was estimated to be 500 with a growth rate of 8% each year. Which of the following models the estimated population of deer in “t” years?

A. P(t)=500(1.08)^t
B. P(t)=500(1.8)^t
C. P(t)=500(0.08)^t
D. P(f)=500(0.82)^t

Respuesta :

Answer:

Step-by-step explanation:

The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^t

Where

A represents the population of the deer after t years.

t represents the number of years.

P represents the initial population of the deer.

r represents rate of growth.

From the information given,

P = 500

r = 8% = 8/100 = 0.08

Therefore, the models that estimates the population of deer in “t” years is

A. P(t)=500(1.08)^t

The model that represents the estimated population of deer in “t” years is Option A. [tex]P(t)=500(1.08)^t[/tex]

Calculation of the models:

Since In 2016 the population of deer in an area was estimated to be 500 with a growth rate of 8% each year.

So, we know that

[tex]A = P(1 + r)^t[/tex]

Here

A Means the population

t means the number of years.

P means the initial population

r means rate of growth.

So, the model is option A.

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A. P(t)=500(1.08)^t