Answer:
The function which is an exponential decay function is:
[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]
Step-by-step explanation:
We know that an exponential function is in the form of:
[tex]f(x)=ab^x[/tex]
where a>0 and if 0<b<1 then the function is a exponential decay function.
and if b>1 then the function is a exponential growth function.
a)
[tex]f(x)=\dfrac{3}{4}(\dfrac{7}{4})^x[/tex]
Here
[tex]b=\dfrac{7}{4}>1[/tex]
Hence, the function is a exponential growth function.
b)
[tex]f(x)=\dfrac{2}{3}(\dfrac{4}{5})^{-x}[/tex]
We know that:
[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]
Hence, we have the function f(x) as:
[tex]f(x)=\dfrac{2}{3}(\dfrac{5}{4})^x[/tex]
Here
[tex]b=\dfrac{5}{4}>1[/tex]
Hence, the function is a exponential growth function.
c)
[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]
We know that:
[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]
Hence, we have the function f(x) as:
[tex]f(x)=\dfrac{3}{2}(\dfrac{7}{8})^x[/tex]
Here
[tex]b=\dfrac{7}{8}<1[/tex]
Hence, the function is a exponential decay function.
d)
[tex]f(x)=\dfrac{1}{3}(\dfrac{9}{2})^x[/tex]
Here
[tex]b=\dfrac{9}{2}>1[/tex]
Hence, the function is a exponential growth function.
