Question

Construct a mathematical model for the following real-life situations(make a table)

Answer 1

The mathematical model representing the scenarios described can be expressed as follows :

• If n ≤ 8 ; A(n) = 31.25n
• If n > 8 ; A(n) = 31.25 + 46.875(n - 8)

• T(n) = 15 + 5(n - 1)

1.)

Amount paid per 8 hours at summer job = 250

Additional hours beyond, 8 hours = 1.5 × hourly rate

Let:

• hourly rate = p
• Number of hours worked = n
• Amount earned as a function of n, A(n)

Hourly rate, p = (250 ÷ 8) = 31.25

Therefore, the hourly rate, p at the summer job = $31.25

Overtime pay = 1.5 × 31.25 = $46.875

Therefore,

If n ≤ 8 ; A(n) = 31.25n

If n > 8 ; A(n) = 31.25 + 46.875(n - 8)

2.)

Let :

• Number of playing hours = n
• Total amount charged as a function of n ; T(n)

Therefore,

T(n) = First hour fee + (charge per additional hour × number of additional hours)

T(n) = 15 + 5(n - 1)

Therefore, the models can be used to calculate the total earning and amount charged for any given hour value.

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