Question

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

Answer 1

Answer:

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.

Step-by-step 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