Question

The invasive cane toad shows a population growth rate of 7% per year. How many years will

it take for this invasive population to grow from 4 million cane toads to 16 million cane
toads?

Please be quick

Answer 1

Given:

Initial population = 4 millions

Growth rate = 7% = 0.07

Present population = 16 millions

To find:

The time it will take for this invasive population to grow from 4 million cane toads to 16 million cane toads.

Solution:

The exponential growth model is

`P=P_0(1+r)^t`

where, P is present population,
`P_0` is iniital population, r is growth rate and t is time in years.

Substitute P=16,
`P_0=4` and r=0.07, we get

`16=4(1+0.07)^t`

Divide both sides by 4.

`4=(1.07)^t`

Taking log on both sides.

`\log 4=\log (1.07)^t`

`\log 4=t\log (1.07)`
`[\because \log x^n=n\log x]`

`(\log 4)/(\log (1.07))=t`

`t=20.4895367`

Approx the value to the next integer.

`t\approx 21`

Therefore, the required number of years is 21.