Question

Mike forgot to replace the cap on a bottle of room freshener. The room freshener began to evaporate at the rate of 15% per day. If the original amount of room freshener in the bottle was 40 grams, which of the following graphs best represents the amount of room freshener 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

For this case we have a function of the form:

`y = A * (b) ^ x`
Where,
A: initial amount
b: decrease rate
x: time in days
Substituting values we have:

`y = 40 * (0.85) ^ x`
Therefore, the graph of the function is a decreasing exponential function in the first quadrant and that has an initial value of 40.
Answer:
graph of exponential function going from left to right in quadrant 1 through the point 0, 40 and approaching the x axis