Question

Jake forgot to replace the cap on a bottle of deodorant. The deodorant began to evaporate at the rate of 12% per day. If the original amount of deodorant in the bottle was 30 grams, which of the following graphs best represents the amount of deodorant f(x) that would remain in the bottle after x days?

graph of function f of x equals 30 multiplied by 0.88 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis
graph of function f of x equals 50 multiplied by 0.82 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis

Answer 1

first one

f(x) = 30(0.88)^x

Answer 2

1. Graph of function f of x equals 30 multiplied by 0.88 to the power of x

Explanation:

We are given that,

Original amount of deodorant in the bottle = 30 grams

The rate of evaporation = 12% = 0.12

That is, we see that the deodorant is decreasing as the number of days increases.

So, the function form of the decrease in the amount of deodorant is given by,

`f(x)=30(1-0.12)^x`, where x is the number of days.

i.e.
`f(x)=30(0.88)^x`, where x is the number of days.

Hence, the graph representing the amount of deodorant after x number of days is,

1. Graph of function f of x equals 30 multiplied by 0.88 to the power of x