Question

Mitchell is an ecologist studying bonobos, a species of ape that lives in the Congolian rainforest. When he started his study, there was a population of about 40,000 bonobos. After one year, he estimated that the population had decreased to 39,200. Based on his data, Mitchell expects the population to continue decreasing each year.

Write an exponential equation in the form y=a(b)x that can model the bonobo population, y, x years after Mitchell began studying them.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
Y=?
To the nearest hundred, what can Mitchell expect the bonobo population to be 7 years after the study began?
--bonobos

Answer 1

P(x)=
`(40000)( 0.98)^x`

A=40000 B=0.98
P(7)= 34700

Explanation:

Notice the population can be modeled as:

P(x)=
`A B^x`

For X=0 P(0)=40000=A (Initial population)
So A=40000
For x=1 (one year after) P=39200

`39200=40000 B^1`
solving for B

`B=(39200)/(40000) =0.98`
So B=0.98

So the population can be modeled as

P(x)=
`(40000)( 0.98)^x`

Now at 7 years:

P(7)=
`(40000)( 0.98)^7`= 34725.02133
Needs to be rounded to the nearest hundred
This is 34700 bonobos (7 years after the study began)