Ebuka’s monthly rent is $750. If Ebuka pays the rent late, his landlord charges 4% interest per week that the payment is late. Write a function that gives the total cost R(t), in dollars, of Ebuka’s rent if he pays it t weeks late.
The Correct Answer and Explanation is:
To formulate the total cost ( R(t) ) of Ebuka’s rent when he pays it ( t ) weeks late, we can start by understanding how the late fees are applied.
Given:
- Monthly Rent: ( 750 ) dollars
- Interest Rate: ( 4\% ) per week
Calculation:
- Interest per week: The interest charged each week is ( 4\% ) of the monthly rent, which can be expressed as:
[
\text{Interest per week} = 0.04 \times 750 = 30 \text{ dollars}
] - Total interest for ( t ) weeks: If Ebuka pays his rent ( t ) weeks late, the total interest incurred over these ( t ) weeks is:
[
\text{Total Interest} = 30 \times t
] - Total cost of rent: The total cost ( R(t) ) after ( t ) weeks will be the sum of the original rent plus the total interest accrued:
[
R(t) = 750 + 30t
]
Final Function:
Thus, the function that gives the total cost ( R(t) ) in dollars of Ebuka’s rent if he pays it ( t ) weeks late is:
[
R(t) = 750 + 30t
]
Explanation:
This function clearly illustrates how the total cost of Ebuka’s rent changes based on the number of weeks he delays payment. The base amount of rent is fixed at $750, and for every week the payment is delayed, an additional $30 is added to this base amount. The linear relationship represented in this function indicates that the longer he waits to pay his rent, the more the total cost accumulates due to the interest charges.
For example, if Ebuka pays his rent 1 week late, the total cost will be:
[
R(1) = 750 + 30 \times 1 = 780 \text{ dollars}
]
If he delays for 4 weeks, the calculation would be:
[
R(4) = 750 + 30 \times 4 = 840 \text{ dollars}
]
This model can help Ebuka understand the financial implications of delaying his rent payments, as it quantitatively shows how quickly the total cost increases with time.