Math Problem Statement
Solution
The image shows a table with data on the average price of a two-bedroom apartment in downtown New York City during the real estate boom from 1994 to 2004. The problem asks to use exponential regression to model the price as a function of time , where represents the number of years since 1994.
The table presents the following dataThe image shows a table with data on the average price of a two-bedroom apartment in downtown New York City during the real estate boom from 1994 to 2004. The problem asks to use exponential regression to model the price as a function of time , where represents the number of years since 1994.
The table presents the following
- (years since 1994): 0, 2, 4, 6, 8, 10
- Price in million dollars: 0.38, 0.40, 0.60, 0.95, 1.20, 1.60
Step 1: Exponential Model
We need to model using an exponential function of the form: Where:
- is the initial value (price at ),
- is the growth rate.
Step 2: Applying Regression
We will perform an exponential regression to find the parameters and . This requires a curve-fitting process using the data points provided.
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Math Problem Analysis
Mathematical Concepts
Exponential Regression
Algebra
Formulas
Exponential model P(t) = P₀ * e^(kt)
Theorems
Curve-fitting for exponential growth
Suitable Grade Level
Grades 11-12
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