To complete the table, we need to write exponential functions based on the initial value and rate (growth or decay). The general formula for an exponential function is:

$f(x) = a \cdot (1 \pm r)^x$

where:

• $a$ is the initial value,
• $r$ is the rate of growth (if positive) or decay (if negative),
• $x$ is the variable (time, typically).

In this context:

• For growth, we use $(1 + r)$.
• For decay, we use $(1 - r)$.

Solutions:

1. Initial Value: 154, Growth Rate: 14% $f(x) = 154 \cdot (1 + 0.14)^x = 154 \cdot (1.14)^x$

2. Initial Value: 490, Growth Rate: 4% $f(x) = 490 \cdot (1 + 0.04)^x = 490 \cdot (1.04)^x$

3. Initial Value: 389, Decay Rate: 3% $f(x) = 389 \cdot (1 - 0.03)^x = 389 \cdot (0.97)^x$

4. Initial Value: 96, Decay Rate: 40% $f(x) = 96 \cdot (1 - 0.40)^x = 96 \cdot (0.60)^x$

Completed Table:

Would you like further details on these calculations or have any specific questions?

Further Questions for Exploration:

1. What would the function look like if the growth rate for 154 was changed to 10%?
2. How does doubling the decay rate for the initial value of 389 affect its function?
3. What is the effect of the initial value on the growth or decay rate outcome over time?
4. How can these exponential functions be used to model real-world scenarios?
5. What is the difference between a growth and a decay function when represented on a graph?

Tip: Remember that a growth factor greater than 1 represents an increase, while a decay factor less than 1 represents a decrease over time.