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Ebuka's monthly rent is $750\$750. If Ebuka pays the rent late, his landlord charges 4%4\% interest per week that the payment is late. Write a function that gives the total cost R(t)R(t), in dollars, of Ebuka's rent if he pays it tt weeks late.

Full solution

Q. Ebuka's monthly rent is $750\$750. If Ebuka pays the rent late, his landlord charges 4%4\% interest per week that the payment is late. Write a function that gives the total cost R(t)R(t), in dollars, of Ebuka's rent if he pays it tt weeks late.
  1. Identify base cost and interest rate: Identify the base cost and the interest rate. Ebuka's monthly rent is $750\$750, and the interest rate is 4%4\% per week for late payment.
  2. Convert interest rate to decimal: Convert the interest rate from a percentage to a decimal. 4%4\% as a decimal is 0.040.04.
  3. Write total cost function: Write the function for the total cost R(t)R(t) of the rent when paid tt weeks late.\newlineThe interest for one week is 0.040.04 times the rent, so for tt weeks, the interest is 0.04×$750×t0.04 \times \$750 \times t.\newlineThe total cost R(t)R(t) is the sum of the base rent and the interest.\newlineR(t)=base rent+(interest rate×base rent×number of weeks late)R(t) = \text{base rent} + (\text{interest rate} \times \text{base rent} \times \text{number of weeks late})\newlineR(t)=$750+(0.04×$750×t)R(t) = \$750 + (0.04 \times \$750 \times t)
  4. Simplify the function: Simplify the function. R(t)=$750+($30t)R(t) = \$750 + (\$30 \cdot t)
  5. Ensure correct form: Ensure the function is in the correct form to answer the question prompt.\newlineThe function R(t)=$(750)+($(30)t)R(t) = \$(750) + (\$(30) \cdot t) correctly represents the total cost of the rent when paid tt weeks late.

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