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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

Respuesta :

Edufirst
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)

Answer:

[tex]f(n)= 24(0.5)^{n-1}[/tex]

Step-by-step 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

[tex]\frac{12}{24} = 0.5[/tex]

[tex]\frac{6}{12} = 0.5[/tex]

[tex]\frac{3}{6} = 0.5[/tex]

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 [tex]f(n)= 24(0.5)^{n-1}[/tex]

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