The image you uploaded shows the formula for calculating the decay rate. Here is the key information from the image:

• The general equation for exponential decay is given as: $y = 2(0.55)^x$
• The decay factor is represented as $b = 1 - r$, where $r$ is the decay rate.

The decay rate, $r$, can be determined by the value of $b$, the base of the exponential function (in this case, $0.55$).

Explanation:

To find the decay rate $r$, we use the formula $b = 1 - r$:

• Given $b = 0.55$ (since $0.55$ is the base of the exponential decay function), $0.55 = 1 - r$
• Solving for $r$: $r = 1 - 0.55 = 0.45$ Thus, the decay rate $r$ is $0.45$, or 45%.

Would you like more details on how to use this equation or any other questions related to decay rates?

Here are some related questions you could explore:

1. How do decay rates affect the exponential decay model?
2. What is the difference between exponential growth and exponential decay?
3. Can you explain the concept of "half-life" in relation to decay rates?
4. How would this decay model change if the base was $0.75$ instead of $0.55$?
5. How can decay rates be used in real-life applications, such as population decline or radioactive decay?

Tip: In exponential decay, the rate $r$ represents the percentage of decay each time unit.