Question

The number of leaves that fall off a tree n days after day 1 is given by the function f (n) = 3(2)".

What does the value 3 mean in this function?

A. On the first day, 3 leaves fall.

OB. 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.

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

A. On the first day, 3 leaves fall.

B. D. The number of leaves that fall on a given day is 2 times the number of leaves that fell on the previous day.

Explanation:

Given

`f(n) = 3(2)^n`

Solving (a) The meaning of 3.

3 represents the initial number of leaves (i.e. the first day) and this proved as follows.

On the first day, n = 0.

Substitute 0 for n in
`f(n) = 3(2)^n`

`f(0) = 3(2)^0`

`f(0) = 3*1`

`f(0) = 3`

Solving (b) The meaning of 2.

2 represents the rate which leaves fall down.

In (a)

`f(0) = 3`

Take n = 1

Substitute 1 for n in
`f(n) = 3(2)^n`

`f(1) = 3(2)^1`

`f(1) = 3*2`

`f(1) = 6`

When f(1) is divided by f(0), the result 2. So, the number of leaves doubles everyday