Question

Midge added some chlorine to the water in a pool. The chlorine evaporated at a fixed rate every week. The table below shows the amount of chlorine f(n), in ounces, that was left in the pool after n weeks: n f(n) 1 16 2 8 3 4 4 2 Which function best shows the relationship between n and f(n)?

Which function best shows the relationship between n and f(n)?
f(n) = 16(0.5)n−1
f(n) = 32(0.5)n−1
f(n) = 16(0.5)n
f(n) = 32(0.5)n+1

Answer 1

Answer is A

Explanation:

Answer 2

Option 1st is correct

`f(n) = 16 \cdot (0.5)^(n-1)`

Explanation:

The nth term for the geometric sequence is given by:

`f(n)=f(1) \cdot r^(n-1)` ....[1]

where,

`f(1)` is the first term

r is the common ratio of the terms.

n is the number of terms.

As per the statement:

Midge added some chlorine to the water in a pool. The chlorine evaporated at a fixed rate every week.

The table below shows the amount of chlorine f(n), in ounces, that was left in the pool after n weeks:

n f(n)

1 16

2 8

3 4

4 2

This is an geometric sequence

For n = 1

From the table:

`f(1) = 16`

r = 0.5

Since,

`(f(2))/(f(1)) = (8)/(16) = 0.5`,

`(f(3))/(f(2)) = (4)/(8) = 0.5`, and so on..

Substitute the value of f(1) = 16 and r = 0.5 in [1] we have;

`f(n) = 16 \cdot (0.5)^(n-1)`

Therefore, the function best shows the relationship between n and f(n) is,
`f(n) = 16 \cdot (0.5)^(n-1)`