Question

A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form f(x) = abx to represent the number of birds after x years. Which values should she use for a and b?

Answer 1

F(x)=240(1.16)^x
a=240
b=1.16

Answer 2

Hence, the function function f(x) is given as:

f(x)=240×(1.16)^x

Explanation:

It is given that:

A population of 240 birds increases at a rate of 16% annually.

i.e. the increase is at a rate of=16/100=0.16

This means that this model can be modeled with the help of an exponential function of the type:

f(x)=ab^x i.e. f(x) represents the number of birds after 'x' years.

where a is the initial population.

and b is the change in the population.

Here we have:

a=240

and b=1+0.16=1.16

Hence, the function function f(x) is given as:

f(x)=240×(1.16)^x