https://file.aiquickdraw.com/mathbot/file/1727472637067lzpv9sol.jpg

The given exponential function is:

\[
y = 51(0.91)^x
\]

### Identifying Growth or Decay
An exponential function has the general form:

\[
y = a(b)^x
\]

- If \( b > 1 \), the function represents exponential growth.
- If \( 0 < b < 1 \), the function represents exponential decay.

In this case, \( b = 0.91 \), which is less than 1. Therefore, the function represents **exponential decay**.

### Determining the Percentage Rate of Decrease
To find the percentage rate of decrease, subtract \( b \) from 1 and then multiply by 100:

\[
\text{Rate of decrease} = (1 - b) \times 100 = (1 - 0.91) \times 100 = 0.09 \times 100 = 9\%
\]

### Answer
The function represents **exponential decay** with a **9% rate of decrease**.

Would you like more details or have any questions?

### Related Questions
1. How would the function change if the base were greater than 1, say 1.05?
2. What is the significance of the coefficient 51 in the given function?
3. How does the rate of change affect the shape of the graph?
4. What is the half-life of a function that decays at a 9% rate per unit of \( x \)?
5. How do you convert exponential decay into a logarithmic form?

### Tip
In exponential functions, always examine the base to quickly determine whether the function represents growth or decay.

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y = 51(0.91)^x

Explore the exponential decay in the function y = 51(0.91)^x, identifying the 9% rate of decrease. This problem covers essential concepts of exponential growth and decay, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation