Question

The elk population in an area is increasing. This year, the population was 1.076 times last year's population of 1537.

Answer 1

Solution:

Original Population of elk= 1537

Population after a year =1537 × 1.076

Let rate at which Population of elk is increasing = R %

Let In the beginning the population of elk= P

t= Time after which population is to be found

E(x)=Population of elk after time t,that is E(0)=P

So, Writing the formula at the rate which population of elk is increasing:

⇒E(x)= $P(1 +\frac{R}{100})^t$

E(1)= 1537

⇒1537=  $P(1 +\frac{R}{100})^1$

1537= $P(1 +\frac{R}{100})$

E(2)= 1537 × 1.076=1653.812

⇒ 1653.812=  $1537(1 +\frac{R}{100})^1$

$\frac{1653.812}{1537}=(1 +\frac{R}{100})^1\\\\ (1.076) =(1 +\frac{R}{100})\\\\ 1.076-1=\frac{R}{100}\\\\ 0.076 \times 100= R \\\\ R= 7.6$

E(9)= 1537 $\times(1+\frac{R}{100})^8$

As P is population when t=0, so we have to find population after 9 years , as $P_{1}$ is population when t=1,so considering $P_{1}$ as initial population, so, t=8

E(9)= $1537 \times (1.076)^8$

      = 1537 × 1.796

      = 2761.6716

     = 2761.68 (Approx)