Question

James rents an apartment with an initial monthly rent of $1,600. He was told that the rent goes up 1.75% each year. Write an exponential function that models this situation to calculate the rent after 15 years. Round the monthly rent to the nearest dollar.

Answer 1

The exponential function to model the increasing rent for James's apartment is R(t) = 1600 × (1 + 0.0175)^t. After substituting t with 15, the calculated rent after 15 years, rounded to the nearest dollar, is $2075.

Step-by-step explanation:

To model the situation where James rents an apartment with an initial monthly rent of $1,600 and the rent increases by 1.75% each year, we use an exponential function. The general form of the exponential function for this scenario is:

R(t) = R_0 imes (1 + r)^t

Where:

• R(t) is the rent after t years,
• R_0 is the initial rent,
• r is the annual increase rate (as a decimal),
• t is the number of years.

Plugging the given values into this formula:

R(t) = 1600 imes (1 + 0.0175)^t

To calculate the rent after 15 years, we substitute t with 15:

R(15) = 1600 imes (1 + 0.0175)^{15}

Using a calculator, we find:

R(15) = 1600 imes (1.0175)^{15}

R(15) = 1600 imes 1.2971

R(15) = 2075.376

Rounded to the nearest dollar, the rent after 15 years is $2075.