Answer:
2) Exponential growth
3) Exponential decay
Step-by-step explanation:
The general form of an exponential function is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{General form of an Exponential Function}}\\\\f(x)=ab^x\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$a$ is the initial value ($y$-intercept).}\\ \phantom{ww}\bullet\;\textsf{$b$ is the base (growth/decay factor) in decimal form.}\end{array}}[/tex]
If a > 0 and b > 1, then the function represents exponential growth.
If a < 0 and b > 1, then the function represents exponential decay.
If a > 0 and 0 < b < 1, then the function represents exponential decay.
If a < 0 and 0 < b < 1, then the function represents exponential growth.
Question 2
[tex]f(x)=2\left(\dfrac{7}{5}\right)^x[/tex]
In this case, a = 2 and b = 7/5. Therefore, as a > 0 and b > 1, then the function represents exponential growth.
Question 3
[tex]f(x)=\dfrac{4}{3}\left(\dfrac{1}{6}\right)^x[/tex]
In this case, a = 4/3 and b = 1/6. Therefore, as a > 0 and 0 < b < 1, then the function represents exponential decay.
