Question

As more people entered the coffee shop, the number of pounds of coffee the employees had in stock decreased every hour.

The function p(x)=0.4(.91)^x models the number of pounds of coffee in hundreds of pounds where x represents the number of hours since the trend has been observed.
What do the values in the function represent?
Select each correct answer.


There were 40 pounds of coffee in stock when the trend began.
The number of pounds of coffee in stock decreased by 91% each hour since the trend began.
There were 400 pounds of coffee in stock when the trend began.
The number of pounds of coffee in stock decreased by 9% each hour since the trend began.
There were 4000 pounds of coffee in stock when the trend began.

Answer 1

There were 40 pounds of coffee in stock when the trend began.

The number of pounds of coffee in stock decreased by 9% each hour since the trend began.

Explanation:

I took the test :)

Answer 2

There were 40 pounds of coffee in stock when the trend began.

The number of pounds of coffee in stock decreased by 9% each hour since the trend began.

Explanation:

We are given the following information in the question:

`p(x) = 0.4(0.91)^x`

where p(x) models the number of pounds of coffee in hundreds of pounds where x represents the number of hours since the trend has been observed.

When x = 0

`p(0) = 0.4(0.91)^0 = 0.4\\\text{Amount of coffee} = 0.4* 100 = 40\text{ pounds}`

Thus, we can say there were 40 pounds of coffee in stock when the trend began.

When x = 1, that is 1 hour after the trend began. The decrease in coffee is given by:

`p(1) = 0.4(0.91)^1 = 0.364\\\text{Amount of coffee} = 0.364* 100 = 36.4\text{ pounds}`

Percentage decrease =

`\displaystyle\frac{\text{Decrease}}{\text{Original}}* 100\% = (40-36.4)/(40)* 100\% = 9\%`

Thus, we can say, the number of pounds of coffee in stock decreased by 9% each hour since the trend began.