Question

The population of a certain animal species you are studying decreases at a rate of 3.5% per year. Only 80 of the animals in the habitat remain after 3 years of conducting your research. What was the initial amount of animals.

Answer 1

Answer:

Therefore the initial amount of animal was 89.

Step-by-step explanation:

Given that,at rate of 3.5% per year, the population of a certain animal species decreases.

The population growth formula:

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

A= number of population after n year.

P= initial population.

n= time in year

r= rate of growth per annum.

Here A=80, P=?, n= 3 years, r= -3.5% = -0.035[ since the rate of growth decrease]

Putting the all values,

$80=P(1-0.035)^3$

$\Rightarrow 80= P(0.965)^3$

$\Rightarrow P=\frac{80}{(0.965)^3}$

      ≈89.

Therefore the amount of animal at its initial stage was 89.