Question

Which is an exponential decay function?

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Answer 1

It is the third one, since the base of the exponent is less than 1, where the exponent is x. 7/4 and 9/2 are greater than 1 and the -x in the second and third choices flip the fraction. So the second one is actually (5/4)^x and the third one is (7/8)^x. Since 7/8 is less than 1, it is an exponential decay function.

Answer 2

The answer is the 3rd equation.

The 1st and 4th equations are growth equations since the fractions are larger than 1. Since the 2nd and 3rd are the only ones with a negative exponent they are the only candidates for a decay function.

The tricky part here is the fraction associated with the negative exponent. Since it is a negative exponent the fraction is going to invert. So the 2nd equation becomes (5/4)^x which becomes a growth function. The 3rd equation has the fraction 8/7 which will become (7/8)^x. This value is smaller than 1 and will continue to shrink as x becomes larger. This is the decay function.