Answer:
[tex]y=(\frac{5}{4})^x[/tex]
[tex]y=5^x[/tex]
Step-by-step explanation:
we know that
In a exponential function of the form
[tex]y=a(b^x)[/tex]
where
a is the initial value
b is the base
If the value of b >1 ----> then is a exponential growth
If the value of b <1 ----> then is a exponential decay
Verify each case
case a) we have
[tex]y=(\frac{5}{4})^x[/tex]
[tex]b=\frac{5}{4}[/tex]
b> 1
therefore
The function represent exponential growth
case b) we have
[tex]y=(4)^{-x}[/tex]
[tex]b=\frac{1}{4}[/tex]
b< 1
therefore
The function represent exponential decay
case c) we have
[tex]y=5^x[/tex]
[tex]b=5[/tex]
b> 1
therefore
The function represent exponential growth
case d) we have
[tex]y=(\frac{4}{5})^x[/tex]
[tex]b=\frac{4}{5}[/tex]
b< 1
therefore
The function represent exponential decay
