Question

Which is an exponential decay function?

f start bracket x end bracket equals Three-fourths start bracket Seven-fourths end bracket superscript x
f start bracket x end bracket equals two-third start bracket Four-fifths end bracket superscript negative x
f start bracket x end bracket equals Three-halves start bracket Eight-sevenths end bracket superscript negative x
f start bracket x end bracket equals one-third start bracket negative nine-halves end bracket superscript x

Answer 1

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

Answer 2

An exponential decay function that is

• Here is the translation that is
• First f(x)= 3/4 (7/4)^+x
• secondly is f(x)= 2/3 (4/5)^-x
• Then third step is f(x)= 3/2 (8/7)^-x
• Last is f(x)= 1/3 (9/2)^+x
• So that is Basically when we have to check if each statement is true.
• That is ^-x= <
• now, ^+x= >
• Now when the 7/4 > 1 is 1.75 > 1, making the statement true. (Positive exponential function)
• So that is 4/5 < 1 is 0.8 < 1, making it true.
• (Positive exponential function)
• After that is  8/7 > 1 is 1.1428.. < 1,  which is making this statement false and also that thus a decay exponential function.  
• Then 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

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