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