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? a = b =

Answer 1

Answer:

a=240

b= 1.16

Step-by-step explanation:

The general form of exponential function for growth is given by:

y = a(1+r)ˣ

We can rewrite it by letting 1+r = b

y= abˣ

a from the given equation represents the initial number of birds, which is given by 240. Hence, a = 240

In (1+r), r is given as the rate of increase, which is given as 16% or 16/100=0.16.

For r = 0.15

b = 1+r

b = 1+ 0.16

b = 1.16

Substituting it in the initial equation:

y = abˣ

y = 240 (1.16)ˣ

where a = 240 and b = 1.16