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.

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