Question

A school has 200 students and spends $40 on supplies for each student. The principal expects the number of students to increase by 5% each year for the next 10 years and wants to reduce the amount of money spent on supplies by 2% for each student each year. Use the drop-down menus to choose or create functions to model:

A. The predicted number of students over time, ()
()=
B. The predicted amount spent per student over time, ()
()=
C. The predicted total expense for supplies each year over time, ()
()= () ___ ()

Answer 1

Explanation:

The predicted number of students over time, S(t)

Rate of increment is 5% per year.

A function 'S(t)' which gives the number of students in school after 't' years.

S(0) means the initial year when the number of students is 200.

S(0) = 200

S(1) means the number of students in school after one year when the number increased by 5% than previous year which is 200.

S(1) = 200 + 5% of 200 = = =

S(2) means the number of students in school after two year when the number increased by 5% than previous year which is S(1)

S(2) = S(1) + 5% of S(1) = = =

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Similarly

The predicted amount spent per student over time, A(t)

Rate of decrements is 2% per year.

A function 'A(t)' which gives the amount spend on each student in school after 't' years.

A(0) means the initial year when the number of students is 40.

A(0) = 40

A(1) means the amount spend on each student in school after one year when the amount decreased by 2% than previous year which is 40.

A(1) = 40 + 2% of 40 = = =

A(2) means the amount spend on each student in school after two year when the amount decreased by 2% than previous year which is A(1)

A(2) = A(1) + 2% of A(1) = = =

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Similarly

The predicted total expense for supplies each year over time, E(t)

Total expense = (number of students) × (amount spend on each student)

E(t) = S(t) × A(t)

(NOTE : The value of x in all the above equation is between zero(0) to ten(10).)