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)= [tex]P(1 +\frac{R}{100})^t[/tex]
E(1)= 1537
⇒1537= [tex]P(1 +\frac{R}{100})^1[/tex]
1537= [tex]P(1 +\frac{R}{100})[/tex]
E(2)= 1537 × 1.076=1653.812
⇒ 1653.812= [tex]1537(1 +\frac{R}{100})^1[/tex]
[tex]\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[/tex]
E(9)= 1537 [tex]\times(1+\frac{R}{100})^8[/tex]
As P is population when t=0, so we have to find population after 9 years , as [tex]P_{1}[/tex] is population when t=1,so considering [tex]P_{1}[/tex] as initial population, so, t=8
E(9)= [tex]1537 \times (1.076)^8[/tex]
= 1537 × 1.796
= 2761.6716
= 2761.68 (Approx)
