Question

An initial population of 505 quail increases at an annual rate of 23%. How do you write an exponential function to model the quail population?

Answer 1

`y = 505(1+0.23)^(t)`

Explanation:

Population growth is seen to increase at an exponential rate. We use the following to model this growth.

`color(white)(aaaaaaaaaaaaa)y = A_(o)(1+r)^(t)`

Where
`"y = value at time (t)"`
`"A"_(o) = "original value"`
`"r = rate of growth"`
`"t = time elapsed"`

An exponential function that models the quail population is set up like...

`color(white)(aaaaaaaaaaaaa)color(orange)(y = 505(1+0.23)^(t)`

so that, for example, if we wanted to figure out the population at time (3 years), then we would set up the function as follows,

`y = 505(1+0.23)^(3)`

to get

`y = 939.3 ~~ 939" quails"` after the `3^(rd)` year has elapsed.