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

The exponential decay function is ⇒ 3rd answer

Step-by-step explanation:

* Lets explain the exponential decay function

- The general form of an exponential Function is ,

 where a is the initial value and b is growth factor

- If b > 1 , then the function is exponential growth function

- If 0 < b < 1 , then the function is exponential decay function

- The function can be written as

# Remember: if 0 < b < 1 , then 1/b > 1 , then change the negative

  sign of the power by reciprocal the growth factor to decide the

  function is growth or decay

* Lets solve the problem

1.

∵ b = 7/4

∵ 7/4 is greater than 1

∴ f(x) is an exponential growth function

2.

- Change the (-x) to x by reciprocal (4/5) to (5/4)

∴

∵ b = 5/4

∵ 5/4 is greater than 1

∴ f(x) is an exponential growth function

3.

- Change the (-x) to x by reciprocal (8/7) to (7/8)

∴

∵ b = 7/8

∵ 7/8 is greater than 0 and smaller than 1 ⇒ 0 < 7/8 < 1

∴ f(x) is an exponential decay function

* The exponential decay function is

domain is all the x values included in the

0 ≤ x ≤ 2

range is all the y values of the graph

-2 ≤ y ≤ 2

***keep in mind that there are different ways to show domain and range

hope this !

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