Question

Which equation represents a population of 370 animals that decrease at an annual rate of 11% ?A. p = 370(1.11)^tB. p= 370(0.11)^ tC. p = 370(0.89) ^tD.p= 370(1.89)^t

Answer 1

Suppose we start with a population of 370. After one year, we have a decrease of 11%. So we will calculate the 11% of 370 and then subtract it from 370. Recall that to calculate the 11% of a number, we can multiply the number by 0.11. Then, the 11% of 370 would be

`370\cdot0.11`

So after one year, we have

`370\text{ - 370}\cdot0.11`

If we factor 370, we get

`370\cdot(1\text{ -0.11)=370}\cdot0.89`

Note that then to calculate a decrease of 11% from one year to anothe we simply multiply by 0.89. So starting at year 0 with 370, after t years we would have

`370\cdot(0.89)^t`