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18 February, 09:10

Hannah is a freshman in college. Her scholarship indicated that each quarter she has $1000 deposited into a meal plan account for her to use to purchase food. Every day Hannah spends $25 on food. Let f (x) represent the amount of money remaining in the account and x represent the number of days.

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  1. 18 February, 09:34
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    f (x) = $1000 - $25*x

    (40 days, $0)

    (0 days, $1000)

    Step-by-step explanation:

    Solution:-

    - Every quarter Hannah receives $1000 in her account for meal plan.

    - So for a quarter of a year she has $1000 to spend.

    - She spends $25 on food each day; hence, an amount of $25 is deducted each day.

    - We can mathematically express the amount remaining in her account after (x) days as follows:

    y = f (x) = Initial deposit - (per day deduction) * x

    Where,

    y: The amount remaining in Hannah's account after x days.

    - The initial amount is the quarterly deposit of $1000 and per day deduction is her buying food each day for $25.

    y = f (x) = $1000 - ($25) * x

    - The thing to note is that the above function f (x) is only defined over the domain of a quarter of year i. e from the first day she receives her amount till the next deposit.

    - The number of days it will take for Hannah to empty her account can be determined from finding the x-intercept or (y = f (x) = 0) using the function defined above:

    f (x) = 1000 - 25x = 0

    x = 1000 / 25

    x = 40 days

    - So it will take 40 days for Hannah to empty her account. As an ordered pair it can be written as:

    (40 days, $0) ... Answer

    - The initial deposit of $1000 corroborates the y-intercept of the function defined f (x). Or we can evaluate the derived function at f (0):

    f (0) = 1000 - 25*0

    f (0) = $1000

    - The ordered pair for the y-intercpet would be:

    (0 days, $1000) ... Answer
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