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

Answer:

B

Step-by-step explanation:

Answer 2

Answer:

The exponential decay function is $f(x)=\frac{3}{2}(\frac{8}{7})^{-x}$ ⇒ 3rd answer

Step-by-step explanation:

* Lets explain the exponential decay function

- The general form of an exponential Function is $f(x)=a(b)^{x}$,

 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 $f(x) = a(b)^{-x}$ can be written as

  $f(x)=a(\frac{1}{b})^{x}$

# 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. $f(x)=\frac{3}{4}(\frac{7}{4})^{x}$

∵ b = 7/4

∵ 7/4 is greater than 1

∴ f(x) is an exponential growth function

2. $f(x)=\frac{2}{3}(\frac{4}{5})^{-x}$

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

∴ $f(x)=\frac{2}{3}(\frac{5}{4})^{x}$

∵ b = 5/4

∵ 5/4 is greater than 1

∴ f(x) is an exponential growth function

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

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

∴ $f(x)=\frac{3}{2}(\frac{7}{8})^{x}$

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