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The image shows a table where you need to determine the initial value and the growth or decay rate as a percentage for each exponential function.

The general form of an exponential function is:

\[
f(x) = a \cdot (b)^x
\]

Where:
- \( a \) is the initial value.
- \( b \) is the growth or decay factor.
  - If \( b > 1 \), it's a growth factor.
  - If \( b < 1 \), it's a decay factor.
  
To find the growth or decay rate as a percentage:
\[
\text{Growth/Decay Rate} = (b - 1) \times 100\%
\]

Now, let’s analyze each function:

1. **\( f(x) = 3621(0.77)^x \)**
   - Initial value: \( a = 3621 \)
   - Decay factor: \( b = 0.77 \)
   - Decay rate: \( (0.77 - 1) \times 100 = -23\% \)

2. **\( h(x) = 4369(1.045)^x \)**
   - Initial value: \( a = 4369 \)
   - Growth factor: \( b = 1.045 \)
   - Growth rate: \( (1.045 - 1) \times 100 = 4.5\% \)

3. **\( g(x) = 737(1.03)^x \)**
   - Initial value: \( a = 737 \)
   - Growth factor: \( b = 1.03 \)
   - Growth rate: \( (1.03 - 1) \times 100 = 3\% \)

4. **\( p(t) = 2822(3)^t \)**
   - Initial value: \( a = 2822 \)
   - Growth factor: \( b = 3 \)
   - Growth rate: \( (3 - 1) \times 100 = 200\% \)

5. **\( f(x) = 3999(1.18)^x \)**
   - Initial value: \( a = 3999 \)
   - Growth factor: \( b = 1.18 \)
   - Growth rate: \( (1.18 - 1) \times 100 = 18\% \)

6. **\( d(t) = 3540(0.91)^t \)**
   - Initial value: \( a = 3540 \)
   - Decay factor: \( b = 0.91 \)
   - Decay rate: \( (0.91 - 1) \times 100 = -9\% \)

Let me know if you would like any clarifications or further details!

Here are 5 related questions you might want to explore:
1. What is the difference between growth and decay in exponential functions?
2. How do changes in the base \( b \) affect the graph of an exponential function?
3. Can exponential decay models be used for financial predictions?
4. What is the role of time \( t \) or \( x \) in exponential growth models?
5. How do you convert exponential growth to continuous growth models?

**Tip**: When interpreting an exponential function, always check whether the base is greater or less than 1 to determine growth or decay.

Given the exponential function, determine the initial value and rate of change as a percent for each function: f(x) = 3621(0.77)^x, h(x) = 4369(1.045)^x, g(x) = 737(1.03)^x, p(t) = 2822(3)^t, f(x) = 3999(1.18)^x, and d(t) = 3540(0.91)^t.

Learn how to find the initial value and growth or decay rate as a percentage for given exponential functions such as f(x) = 3621(0.77)^x, h(x) = 4369(1.045)^x, and others. This guide explains key concepts of exponential growth and decay and provides step-by-step solutions for each problem.

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