In the question , it is given that the population is decreasing by 4% per year .
So we have to use the following formula of exponential decay:
[tex] P(t) = P_{0} (1-r)^t [/tex]
Substituting the given values, we will get
[tex] 170 = 200(1-0.04)^t
[/tex]
Dividing both sides by 200
[tex] \frac{170}{200} = (0.96)^t [/tex]
Taking log on both sides
[tex] log (\frac{170}{200}) =log (0.96)^t [/tex]
[tex] log (\frac{170}{200}) =t*log (0.96) [/tex]
Dividing both sides by log(0.96)
[tex] \frac{ log (\frac{170}{200}) }{log(0.96) } =t [/tex]
t = approx 4 years
So after 4 years , the population will be less than 170.
