Question

Given the following equation of an exponential function, determine the decay rate. 0.535e −0.07x:

A. 0.535%
B. 10.5%
C. 50%
D. 46.5%

Answer 1

The exponential function's decay rate, calculated as the percentage decrease per unit time, is 50.00%. None of the provided options precisely matches this value. Option C is the correct choice.

Certainly, here's a step-by-step calculation of the decay rate:

1. Define the Exponential Function:

`\[ f(x) = 0.535e^(-0.07x) \]`

2. Calculate the Initial Value:

`\[ y_0 = f(0) = 0.535 \]`

3. **Calculate the Time to Decay to Half:

`\[ t_{\text{half}} = (\log(0.5))/(-0.07) \approx 9.9021 \]`

4. Calculate the Decay Rate per Unit Time:

`\[ \text{decay\_rate} = 1 - \frac{f(t_{\text{half}})}{y_0} = 0.5000 \]`

5. Convert the Decay Rate to Percentage:

`\[ \text{decay\_rate\_percent} = \text{decay\_rate} * 100 = 50.00\% \]`

Therefore, the decay rate of the function is 50.00% per unit time. Option C is the correct choice.