Final answer:
The value of a house in t years, initially costing $175,000 with a 3% annual increase, can be represented by the function Future Value = $175,000 × (1 + 0.03)^t. This exponential growth formula accounts for the initial value and growth rate.
Step-by-step explanation:
To write a 1-point function that represents the value of a house in t years, given an initial cost and an annual percentage increase, one can use the formula for exponential growth, which takes into account the initial value and the growth rate. In this scenario, the house initially costs $175,000 and gains 3% of its value every year.
The formula for the future value of the house is as follows:
Future Value = Initial Cost × (1 + Growth Rate)^t
Where:
- Initial Cost is $175,000
- Growth Rate is 3%, or 0.03
- t is the number of years in the future
Plugging these values into the formula gives us:
Plugging these values into the formula gives us:
Future Value = $175,000 × (1 + 0.03)^t
So, if a student wants to find out the value of the house after, for example, 5 years, they would calculate:
Future Value = $175,000 × (1 + 0.03)^5
By using this function, one can determine the anticipated value of the house at any point in time t years into the future, taking into account the consistent 3% yearly increase.