Question

Determine if the function is an example of exponential growth or exponential decay:A) f(x) = (1/3)^xB)f(x) =8^xC) f(x) =0.3^x

Answer 1

a) decay

b) growth

c) decay

Explanation:

Exponential function is given as:

$y=ab^x$

To determine if the function is an exponential growth or decay:

when a is positive and b is greater than 1, it is a growth

when a is positive and b is less than 1, it is a decay

$\begin{gathered} a)\text{ f(x) = (}\frac{1}{3})^x \\ a\text{ in this case 1 (positive)} \\ b\text{ = 1/3 (it is less than 1)} \\ \text{Hence, it is a decay} \end{gathered}$$\begin{gathered} b)f(x)=8^x \\ a\text{ in this case 1 (positive)} \\ b\text{ = 8 (it is greater than 1)} \\ \text{Hence, it is a growth} \end{gathered}$$\begin{gathered} c)\text{ }f\mleft(x\mright)=0.3^x \\ a\text{ in this case 1(positive)} \\ b\text{ = 0.3 (it is less than 1)} \\ \text{Hence, it is a decay} \end{gathered}$