Question

13. Erica has a home that is appreciating in value over the past 4 years. The data for the growth of her home'svalue is shown below.lifelongAlgebra 1BCredit 5L4L - Algebra 1B (2020) Page 51YearAmount2016$400,0002017I$420,0002018$441,00020195463,050What kind of function can be used to best represent this data linear, quadratic or exponential? Explain yourreasoning (2 points)

Answer 1

Mathematical Models

Given a set of two-variable data, we can tell if there is a linear relationship between them by analyzing the change of values of y with respect to the change of values of x.

If the relationship was linear, the change in values of y should be the same when the change in x is equal.

Note that between 2016 and 2017 there was only one year and the value of the house increased by $20,000.

For the next two years, the value increased by $21,000. This means the relationship is not linear.

The possible exponential relationship is also easy to spot. If the ratio between the values of y is constant, then it's an exponential function.

Testing the ratios:

420,000 / 400,000 = 1.05

441,000 / 420,000 = 1.05

463,050 / 441,000 = 1.05

Since the ratio is constant, the growth can be modeled with an exponential function.