Question

The number of leaves that fall off a tree n days after day 1 is given by the function f (n) = 3(2)*.
Part A
What does the value 3 mean in this function?
A.
On the first day, 3 leaves fall.
B. On the second day. 3 leaves fall.
• c. The number of leaves that fall on a given day is 3 times the number of leaves that fell on the first day.
D. The number of leaves that fall on a given day is 3 times the number of leaves that fell on the previous day.
+
Part B
What does the value 2 mean in this function?
• A. On the first day, 2 leaves fall.
• B. On the second day, 2 leaves fall.
• C. The number of leaves that fall on a given day is 2 times the number of leaves that fell on the first day.
• D. The number of leaves that fall on a given day is 2 times the number of leaves that fell on the previous day.

Answer 1

Let's clarify the function \( f(n) = 3(2)^n \).

### Part A
The value 3 in the function represents the initial number of leaves that fall when \( n = 0 \). Therefore:

**Correct Answer:**
**A. On the first day, 3 leaves fall.**

### Part B
The value 2 in the function means that for each subsequent day, the number of leaves that fall doubles compared to the previous day. The function result increases as \( n \) increases, indicating exponential growth based on the base of 2.

**Correct Answer:**
**D. The number of leaves that fall on a given day is 2 times the number of leaves that fell on the previous day.**