Identify if the exponential function is growth or decay and justify your response,

4. f(x) = 0.2(1.3)^x
Exponential
Growth or Decay

Respuesta :

Answer:

Exponential growth

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.

Given exponential function:

[tex]f(x)=0.2\left(1.3\right)^x[/tex]

In this case, a = 0.2 and b = 1.3.

Therefore, as a > 0 and b > 1, then the function represents exponential growth.

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