Jerome’s teacher gave him a homework assignment on solving equations. Since he’s been thinking about saving for a used car, he decided to use the assignment as an opportunity to model a savings plan. He already has $500, and he plans to save $375 every month. To model the situation, he created this equation, where y represents the total amount saved for the car and x represents the number of months since he started saving: 500 + 375x = y. He then solved the equation to determine how many months he would need to save to have enough to purchase the car. Review his work, and select the error.

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

for future students the answer is b

hope i

-lavira: )

just took the test and my answers down below!

step-by-step explanation:

check the pic :