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balu736 [363]
3 years ago
15

A population of 200 animals is decreasing by 4% per year. At this rate, in how many years will the population be less than 170?

Mathematics
2 answers:
djyliett [7]3 years ago
8 0
The population will be less that 170 in 4 years
polet [3.4K]3 years ago
5 0

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:

P(t) = P_{0} (1-r)^t

Substituting the given values, we will get

170 = 200(1-0.04)^t

Dividing both sides by 200

\frac{170}{200} = (0.96)^t

Taking log on both sides

log (\frac{170}{200}) =log (0.96)^t

log (\frac{170}{200}) =t*log (0.96)

Dividing both sides by log(0.96)

\frac{ log (\frac{170}{200}) }{log(0.96) } =t

t = approx 4 years

So after 4 years , the population will be less than 170.


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