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

Answer 1

Answer:

graph of function f of x equals 30 multiplied by 0.88 to the power of x

Step-by-step explanation:

The deodorant is begun to evaporate in other words, it is losing mass so the rate of 12% is a decay rate.  In the exponential decay, the graph of the function goes according to the formula:

$y=a(1-r)^x$

Where $a$ is the initial amount ($a=30$), $r$ is the rate of decay ($r=0.12$) and $x$ the times intervals, in this case, measured in days. Substituting the values in the formula:

$y=30(1-0.12)^x\\y=30(0.88)^x$

Which corresponds with the "graph of function f of x equals 30 multiplied by 0.88 to the power of x".