Question

Which is an exponential decay function?

Answer 1

Answer:

The answer is f(x)= $\frac{3}{2}$ $(\frac{8}{7}) x^{-x}$

Explanation:

Now since an exponential decay function is f(x) = $abx^{x}$

The base is 0 < x < 1

Which means the base greater than 0, but less than 1.

So In this problem, the ones with the positive exponent are exponential growth. But we need a decay. So with the negative exponents, you do the reciprocal on the base. Then you would close out the negative exponent. Than you would see $\frac{7}{8}x^{x}$. And it's greater then 0 and less then 1.

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- Sweet queen

Answer 2

I think this question already have an answer that is answered on this but I will still solve it:
Here is the translation:
f(x)= 3/4 (7/4)^+x
f(x)= 2/3 (4/5)^-x
f(x)= 3/2 (8/7)^-x
f(x)= 1/3 (9/2)^+x

Basically you have to check if each statement is true.
^-x= <
^+x= >

7/4 > 1 is 1.75 > 1, making the statement true. (Positive exponential function)

4/5 < 1 is 0.8 < 1, making it true.
(Positive exponential function)

8/7 > 1 is 1.1428.. < 1, making this statement false and thus a decay exponential function.

9/2 > 1 is 4.5 > 1, making it true.
(Positive exponential function)

The answer is the third option:
f(x)= 3/2 (8/7)^-x