FITNESS A fitness center has set a goal to have 500 members. The fitness center already has 150 members and adds an average of 25 members per month. The function
f(x) = 150 + 25r represents the membership after x months. Graph the function to
determine the number of months it will take for the fitness center to reach its
membership goal. Is the function continuous or discrete? Explain.
O a. 14 months; discrete: There cannot be partial members.
Ob 12 months; discrete: There cannot be partial members.
Oe. 13 months; discrete: There cannot be partial members.
Od. 14 months; continuous: There can be partial members.

3

step-by-step explanation:

divide 13.5 by 9 to get the scale factor. it equals 1.5

2 * 1.5 = 3

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt