30 points
4. juanita is planting a garden. she bought one bag of soil and 5 different pots of flowers to
plant. the bag of soil cost $5.00. after using a $4.00 coupon, she spent a total of $12.25.
write an equation to model this situation and find the cost of each pot of flowers. show all
of your work

13

Step-by-step explanation:

because 12+5=17 which is what she spent and 17-4=13 because she had a coupon of 4 dollor off

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