Question

- Bruce 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 54 2 27 3 13.5 4 6.75 Which function best shows the relationship between n and f(n)?.

Answer 1

f (n) = 54 (0.5)^(n-1)

Explanation:

Answer 2

To solve this problem, let us first remember that the formula for rate is:

rate = f (n) = A (r)^(n-1)

Where,

A = the 1st term

r = fractional rate of evaporation

n = number of terms

Now let us calculate for the fraction rate of evaporation, r. Since it is stated that the evaporation is happening at a fixed rate, therefore we can use any two given f (n) values to find for r. In this case, let us use when n=1 and 2.

r = 27 / 54

r = 0.5

The first term in the series is when n = 1 and that is:

A = 54

Therefore substituting all known values to the equation:

f (n) = 54 (0.5)^(n-1) (ANSWER)