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.