Question

Greg made pudding every weekend. The more times he made pudding, the more practice he gained. The time he took to make the same amount of pudding every week decreased with practice. The function below shows the number of hours f(x) Greg took to make pudding after he had made it x times: f(x) = 2(0.8)x Which graph best represents the function?

Answer 1

Here, the number of hours ∝ the number of times he did practice

And, this relation is described by the function,

`f(x) = 2(0.8)^x`

Where, x is the number of times

f(x) is the number of hours.

The above function f(x) is an exponential function.

Having the y-intercept = (0,2)

But it does not have x-intercept.

End Behaviour:

Since 0.8 < 1

Therefore, the end behaviour of the function f(x) is,

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

And, as
`x\rightarrow \infty`,
`f(x)\rightarrow 0`

Thus, from the above information we can plot the graph of the given function. (shown below)

Answer 2

Pls. see attachment.