To solve the given problem, let's analyze the function provided:

$f(t) = 4800(0.84)^t$

This is an exponential decay function where:

• $f(t)$ represents the number of board feet consumed monthly after $t$ months.
• The initial amount of board feet consumed (when $t = 0$) is given by the coefficient 4800.
• The multiplier or decay factor is 0.84.

From this function, we can extract the required values:

1. The number of board feet consumed initially: This is the value of $f(t)$ when $t = 0$. $f(0) = 4800(0.84)^0 = 4800$ So, the number of board feet consumed initially is 4800 board feet.

2. The multiplier: This is the base of the exponential function, which is 0.84.

Therefore:

• The number of board feet consumed initially is 4800 board feet.
• The multiplier is 0.84.

Would you like further details or have any other questions? Here are some questions you might ask:

1. How does the function change if the multiplier is different?
2. What is the significance of the multiplier being less than 1?
3. Can you show the calculation for a specific value of $t$?
4. How does this function model real-world scenarios?
5. What happens to the consumption after a long period (large $t$)?

Tip: When dealing with exponential functions, the coefficient represents the initial value, and the base of the exponent represents the growth or decay rate.