Question

A population of deer triples every two years.It started with five deer.Which function represents the population of deer P in the national park after t number of years.

Answer 1

Answer:

Therefore the required function is

$P=5(\sqrt{3})^t$

Step-by-step explanation:

Given that , a population of deer triple every 2 years.

General growth formula is

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

A= population after t years.

P= initial population

r= rate of increase

t = time.

Given it started with 5 deer.

After 2 years, the number of deer= 15

Putting A=15, P=5,and t=2

$15=5(1+r)^2$

$\Rightarrow (1+r)^2=\frac{15}{5}$

$\Rightarrow 1+r=\sqrt{3}$

$\Rightarrow r=\sqrt{3}-1$

After t year the population of deer is P

Now, A=P, P=5 , t=t and $r=\sqrt{3}-1$

$P=5(1+\sqrt{3}-1)^t$

$\Rightarrow P=5(\sqrt{3})^t$

Therefore the required function is

$P=5(\sqrt{3})^t$