Respuesta :
Answer:
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 Â
