Question

Determine whether the function $y=0.4{\left(\frac{1}{3}\right)}^x$represents exponential growth or decay.

Short answer

The given function $y=0.4{\left(\frac{1}{3}\right)}^x$ representsexponential decay.

Step-by-step solution

Step 1. Write down the given information.

The given function is $y=0.4{\left(\frac{1}{3}\right)}^x$.

Step 2. Concept used.

The exponential function is of the form $y=a{b}^x$ represents exponential growth if the base $b>1$ and exponential decay if the base $0<b<1$ for all $a>0$.

Step 3. Explanation.

From the concept stated above it can be interpreted that the function $y=0.4{\left(\frac{1}{3}\right)}^x$ will represent exponential decay because the base (b) of the function $y=0.4{\left(\frac{1}{3}\right)}^x$ is such that $0<b<1$. Hence, the given function $y=0.4{\left(\frac{1}{3}\right)}^x$ represents exponential decay.

Step 4. Conclusion.

The given function $y=0.4{\left(\frac{1}{3}\right)}^x$ represents exponential decay.