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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.

Sagot :

MrRoyal

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

[tex]f(n) = 3(2)^n[/tex]

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 [tex]f(n) = 3(2)^n[/tex]

[tex]f(0) = 3(2)^0[/tex]

[tex]f(0) = 3*1[/tex]

[tex]f(0) = 3[/tex]

Solving (b) The meaning of 2.

2 represents the rate which leaves fall down.

In (a)

[tex]f(0) = 3[/tex]

Take n = 1

Substitute 1 for n in [tex]f(n) = 3(2)^n[/tex]

[tex]f(1) = 3(2)^1[/tex]

[tex]f(1) = 3*2[/tex]

[tex]f(1) = 6[/tex]

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

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