Question

chang 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 24 2 12 3 6 4 3 which function best shows the relationship between n and f(n)? f(n) = 48(0.5)n−1 f(n) = 24(0.5)n f(n) = 24(0.5)n−1 f(n) = 48(0.5)n 1

Answer 1

`f(n)= 24(0.5)^(n-1)`

Explanation:

the table below shows the amount of chlorine

f(n), in ounces, that was left in the pool after n weeks:

n 1 2 3 5

f(n) 24 12 6 3

We can see that the value of f(n) is decreasing

f(n) does not have common difference. Lets find common ratio

`(12)/(24) = 0.5`

`(6)/(12) = 0.5`

`(3)/(6) = 0.5`

General rule is f(n) = a1 + (r)^(n-1)

Where a1 represents the first term = 24

r represents the common ratio = 0.5

So the function becomes
`f(n)= 24(0.5)^(n-1)`

Answer 2

n f(n)
1 24 f(1) = 24 (0.5)^0
2 12 f(2) = 24 (0.5)^1
3 6 f(3) = 24 (0.5)^2
4 3 f(4) = 24 (0.5)^3

f(n) = 24 [0.5]^(n-1)