One hiking club charges $16 to become a member and $3 to participate on each hike. another club charges no membership fee, but charges $5 to participate on each hike. how many hikes must you go on to make the first club more economical?

x < 8

Step-by-step explanation:

x= # of hikes

3x +16 =5x

-3x. -3x

16=2x

16/2= 8

2x/2= x

8=x

x=8

check:

3(8) +16 =5(8)

24 +16 =40

40=40 ✓

there for at 8 hikes with either deal it would be the same but if you went up a number of hikes for the first option it would only be $43.00 spent in total. but with the second option it would be $45.00.

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

the first option i believe

step-by-step explanation: