Question

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.
\[R(t)=\]

Answer 1

To determine the total cost \(R(t)\) of Ebuka's rent if he pays it \(t\) weeks late, you can start with his base rent of \$750 and then add the interest charged on that rent for each week it is late.

The interest rate is given as \(4\%\) per week. This can be expressed as a fraction: \(0.04\). Therefore, for each week late, the interest charged would be \(0.04 \times 750\).

The total rent after \(t\) weeks late can be calculated as:

\[
R(t) = 750 + (0.04 \times 750 \times t)
\]

Now, simplify the expression:

1. Calculate the interest charged per week:
\[
0.04 \times 750 = 30
\]

This means for each week that the rent is late, he incurs an additional \$30 in charges.

2. Now substitute this back into \(R(t)\):
\[
R(t) = 750 + 30t
\]

Now, we can present the final function:

\[
R(t) = 750 + 30t
\]

This function \(R(t)\) gives the total cost of Ebuka's rent if he pays it \(t\) weeks late.