Chapter 6.4, Problem 43E

To determine

Whether the function represents exponential growth or exponential decay. Identify the percent rate of change.

Answer to Problem 43E

The function represents exponential decay and the rate of decay is $5\%$ .

Explanation of Solution

Giveninformation:

The exponential function is $y=30{(0.95)}^t$ .

The function is of the form $y=a{\left(1-r\right)}^t$ , where $1-r<1$ . Thus, the function represents the decay. Now, using the decay factor

  $1-r=0.95\Rightarrow r=0.05=5\%$ .

Conclusion:

Therefore, the function represents exponential decay and the rate of decay is $5\%$ .