Show that `h(x) = 36(1 - 6^x)` is a decay function. 

2 Answers

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lemjay | High School Teacher | (Level 3) Senior Educator

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Take note that a decay function is a decreasing function. It means as the value of x increases, the value of y decreases.

So to determine if it is a decay function, plug-in values to x and solve for the corresponding value of y.






`y =36(1-6^0)=0`







So we have:

x | -2     -1     0       1         2             10

y | 35     30     0    -180   -1260     -2176782300

Notice that as the values of x increases the values of y decreases.

Hence, `h(x) = 36(1-6^x)` is a decay function.

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rachellopez | Student, Grade 12 | (Level 1) Valedictorian

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A decay function is when x-values increase and y-values decrease. You can prove that `h(x)=36(1-6^(x))` is a decay function by simply plugging in numbers for x. You really don't need to do more than 3 values to see the trend. I'll start with 1.

`h(x)=36(1-6^(1))=-180 `. So you know when x=1, y=-180.

`h(x)=36(1-6^(2))=-1260 `. When x=2, y=-1260. The y value decreased.

`h(x)=36(1-6^(3))=-7740 `. When x=3, y=-7740.

By now you can tell that as x increases, y decreases which fits the definition of a decaying function.