Question

Danielle has decided to raise rabbits but has been warned that the number of rabbits she will have will grow very quickly. Danielle started out with 15 rabbits and the function y = 15 • 1.8x models the number of rabbits she will have after x months. Which graph represents this function?

Answer 1

Here the given function that describes the number of rabbits after x months,

`y = 15 (1.8)^x`

is an exponential function. ( increasing)

Having the y-intercept = (0,15)

But does not have the x-intercept.

End behaviour :

Since, 1.8 > 1

Thus the end behavior of the the function is,

As
`x\rightarrow -\infty`,
`f(x)\rightarrow 0`

And, as
`x\rightarrow \infty`,
`f(x)\rightarrow \infty`

Thus, from the above explanation we can plot the graph of the given function.

Answer 2

Given the function

`y=15(1.8)^x`
The graph representing the function is attached below.