Question

Suppose a daily exponential growth rate for humans is 0.008 while that for rats is 0.037. If we start at time 0 with two pairs of humans and one pair of rats, about how many humans will there be by the time there are one million rats?

Answer 1

ANSWER :-

We can simply use the formula for exponential growth (A = A0 × ekt )

Where,

A = Final population

A0 = Starting population

k = exponential growth rate

t= time in years

For the rats, the starting numbers are 2 (1 pair). We need to find out the time required to reach a size of 1 million rats.

So, A = A0 × ekt

109 = 2 × e(0.037)(t)

(5×108) = e(0.037)(t)

Taking log on either side, we get

ln (5×108) = ln(e0.037t)

20.03 = (0.037) × t

t = 20.03/0.037

t = 541.35 years

Now, we need to find out the final population of humans after 541.35 years.

A = A0 × ekt

A = 4 × e(0.008)(541.35)

​​A = 4 × e(4.3308)

A = 4 × 76.0050

A = 304.02

So, the final population of humans at the time when there are one million rats will be 304.02 ≈ 304.

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