Question

A population of 430,000 toads is expected to shrink at a rate of 5.5% per year.

Which is the best prediction for the toad population in 14 years?

Answer 1

194,766

Explanation:

took the test

Answer 2

`n(t)\approx 190000 toads`Consider the exponential decay model.
In general where
`n(t)` is the number of toads after time
`t` years,
`\alpha` is the initial number of toads, and
`r` is the growth rate of the toads,


`\alpha = 430000`

`r=1-0.055=0.945` [100%-5.5%]

`n(t)=\alpha r^t`

`n(t)=430000*0.945^t`


`\therefore n(14)=430000* 0.945^(14)`

`n(t)=194766.2824...\approx 194766 toads`

Since your question is written to 2 significant figures,

`n(t)\approx 190000toads`