Question

A student has a savings account with $475 in it. She deposits $125 of her paycheck into the account every week. Her goal is to save $7,000 for college.
a.How much will be in the account after 3 weeks?
b.How long will it take before she has $1,350?
c.Write an equation that represents the relationship between the dollar amount in her account and the number of weeks since she started depositing $125 each week.
d.Graph your equation using graphing technology. Mark the points on the graph that represent the amount after 3 weeks, and also the week she has $1,350. Write down the coordinates.
e. How long will it take her to reach her goal?

Answer 1

9514 1404 393

Answer:

  a. $850

  b. 7 weeks

  c. f(x) = 125x +475

  d. see attached (3, 850), (7, 1350)

  e. 53 weeks

Step-by-step explanation:

a.

After 3 weeks, $125×3 = $375 will have been added to the $475 already in the account. The balance will be ...

  $375 +475 = $850

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b.

The student will have to add $1350 -475 = $875 to her account to reach $1350. At a rate of $125 per week, that will take ...

  $875/($125/week) = 7 weeks

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c.

The initial value is $475, and the rate of change is $125 per week, so the equation can be written ...

  f(x) = 475 +125x . . . . . . . balance after x weeks

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d.

See the attached graph with the required points marked. (3, 850), (7, 1350)

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e.

It will take more than 53 weeks for the student to reach her goal. (After 52 weeks, the account will have $6975, so will be $25 short of the goal.)