In this problem, we have an exponential growth function given by:

$f(x) = 87(1.8)^x$

Let's break down each part of the question.

1. Initial Value: The initial value in an exponential function of the form $f(x) = a \cdot b^x$ is represented by $a$. Here, $a = 87$. So, the initial value is 87.

2. Growth Factor: The growth factor in an exponential function is the base of the exponent, which is $b$. In this case, $b = 1.8$. Therefore, the growth factor is 1.8.

3. Growth Rate: To find the growth rate as a percentage, we need to express the growth factor as a rate. The growth rate is calculated as: $\text{Growth Rate} = (b - 1) \times 100\%$ Substituting $b = 1.8$, $\text{Growth Rate} = (1.8 - 1) \times 100\% = 0.8 \times 100\% = 80\%$

Therefore:

• Initial Value: 87
• Growth Factor: 1.8
• Growth Rate: 80%

Would you like further details or explanations?

Here are some related questions:

1. What would the function look like if the growth rate was only 50%?
2. How does changing the initial value affect the function's graph?
3. What happens to the growth rate if the growth factor is less than 1?
4. How can we identify decay versus growth in an exponential function?
5. What is the impact of changing the growth factor to 2?

Tip: In exponential functions, if the growth factor is greater than 1, it indicates growth. If it’s between 0 and 1, it represents decay.