Question

A house that costs $200,000 will appreciate (increases) in value by 3% each year. write a function that models the cost of the house over time. how much will the house be worth in 5 years?

Answer 1

The cost of the house over time can be modeled using the formula C(t) = P(1 + r)^t, where C(t) is the cost of the house at time t, P is the initial cost of the house, r is the annual appreciation rate, and t is the number of years. In this case, the house will be worth approximately $231,859.63 after 5 years.

Step-by-step explanation:

The cost of the house can be modeled using the formula:

C(t) = P(1 + r)^t

where C(t) is the cost of the house at time t, P is the initial cost of the house, r is the annual appreciation rate (expressed as a decimal), and t is the number of years.

In this case, the initial cost of the house is $200,000 and the annual appreciation rate is 3%, or 0.03. Plugging these values into the formula, we have:

C(t) = 200,000(1 + 0.03)^t

To find the value of the house after 5 years, we substitute t = 5 into the formula:

C(5) = 200,000(1 + 0.03)^5

C(5) = 200,000(1.03)^5

Using a calculator, we can evaluate the expression to find that the house will be worth approximately $231,859.63 after 5 years.