A house was purchased for $350,000 in the year 2019. The value has been increasing at a rate of 2% per year.

Write the function that describes the value (y), t years after 2019. 

y=abt


The value of the house is increasing at a rate of 2% per year. This is an example of exponential growth, which can be modeled by the equation:

\[
y = ab^t
\]

Where:
- $y$ is the value of the house after $t$ years.
- $a$ is the initial value of the house (in 2019).
- $b$ is the growth factor per year.
- $t$ is the number of years after 2019.

Given that:
- The initial value of the house $a = 350,000$.
- The growth rate is 2%, which means the growth factor $b = 1 + 0.02 = 1.02$.

Thus, the function that describes the value of the house $y$, $t$ years after 2019 is:

\[
y = 350,000 \cdot (1.02)^t
\]

Would you like a detailed explanation of how exponential growth works or have any specific questions?

Here are 5 related questions for further practice:
1. What will the value of the house be in 2024?
2. How long will it take for the house's value to reach $400,000?
3. What would the value be if the annual growth rate were 3% instead of 2%?
4. How would the equation change if the house were depreciating at a rate of 2% per year?
5. What is the percentage increase in the house’s value over a period of 10 years?

**Tip:** Exponential growth occurs when a quantity increases by the same percentage every period, which is why it can model continuous growth such as housing prices.

A house was purchased for $350,000 in the year 2019. The value has been increasing at a rate of 2% per year. Write the function that describes the value (y), t years after 2019.

Explore how to model the value of a house purchased for $350,000 in 2019, growing at a rate of 2% annually. Learn the exponential growth formula y = 350,000 * (1.02)^t and apply it to real-world scenarios. Ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation