Question

Which equations and graphs represent exponential decay?



(: Use your graphing calculator to see the graphs).

(Select all that apply.)

"y" equals 5 Superscript, "x" , Baseline

"y" equals 0.5 times 8 Superscript, "x" , Baseline

"y" equals 11 times 0.2 5 Superscript, "x" , Baseline

Answer 1

To determine which equations represent exponential decay, we need to look for specific characteristics of exponential functions.

1. **Exponential decay** occurs when the base of the exponential function is a number between 0 and 1. The general form of an exponential function is:

\[
y = ab^x
\]

where \( a \) is a positive constant, and \( 0 < b < 1 \).

Let's analyze each equation:

1. **Equation:** \( y = 5^x \)

- Here, the base \( 5 \) is greater than \( 1 \). This represents exponential growth, not decay.

2. **Equation:** \( y = 0.5 \times 8^x \)

- The base \( 8 \) is also greater than \( 1 \). This represents exponential growth (multiplying by a factor greater than 1), not decay.

3. **Equation:** \( y = 11 \times 0.25^x \)

- The base \( 0.25 \) (which is \( \frac{1}{4} \)) is between \( 0 \) and \( 1 \). This represents exponential decay because the value of \( y \) decreases as \( x \) increases.

### Summary

The equation that represents exponential decay is:

- \( y = 11 \times 0.25^x \)

The other equations do not represent exponential decay.