Math Problem Statement

The following table shows the average price of a two-bedroom apartment in downtown New York City during the real estate boom from 1994 to 2004. Use exponential regression to model the price P(t) as a function of time t since 1994.

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 P(t)P(t) as a function of time tt, where tt 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 P(t)P(t) as a function of time tt, where tt represents the number of years since 1994.

The table presents the following

  • tt (years since 1994): 0, 2, 4, 6, 8, 10
  • Price P(t)P(t) in million dollars: 0.38, 0.40, 0.60, 0.95, 1.20, 1.60

Step 1: Exponential Model

We need to model P(t)P(t) using an exponential function of the form: P(t)=P0ektP(t) = P_0 e^{kt} Where:

  • P0P_0 is the initial value (price at t=0t = 0),
  • kk is the growth rate.

Step 2: Applying Regression

We will perform an exponential regression to find the parameters P0P_0 and kk. 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