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The table below lists the number of homes sold by a real estate company in 2010 and 2015. Let t = the number of years after 2010 and n(t) = the number of homes sold t years after 2010. Years after 2010, t Number of homes sold, n(t) 0 200 5 645 a. Write a linear model n(t)= mt+b for the number of homes sold t years after 2010. b. Use your linear model to predict in which year the number of homes sold will reach (or did reach) 5000 homes. State the year. C. Write an exponential model n(t)=ne" for the number of homes sold t years after 2010. Round the value of r to 5 decimal places in your model. d. Use your exponential model to predict in which year the number of homes sold will reach (or did reach) 5000 homes. State the year.

The table below lists the number of homes sold by a real estate company in 2010 and 2015. Let t = the number of years after 2010 and n(t) = the number of homes sold t years after 2010. Years after 2010, t Number of homes sold, n(t) 0 200 5 645 a. Write a linear model n(t)= mt+b for the number of homes sold t years after 2010. b. Use your linear model to predict in which year the number of homes sold will reach (or did reach) 5000 homes. State the year. C. Write an exponential model n(t)=ne" for the number of homes sold t years after 2010. Round the value of r to 5 decimal places in your model. d. Use your exponential model to predict in which year the number of homes sold will reach (or did reach) 5000 homes. State the year.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Real Estate Sales Analysis and Model Predictions The table below lists the number of homes sold by a real estate company in 2010 and 2015. Let \( t \) = the number of years after 2010 and \( n(t) \) = the number of homes sold \( t \) years after 2010. #### Table: Homes Sold by Year | Years after 2010, \( t \) | Number of homes sold, \( n(t) \) | |---------------------------|----------------------------------| | 0 | 200 | | 5 | 645 | --- #### a. Linear Model Formulation Write a **linear** model \( n(t) = mt + b \) for the number of homes sold \( t \) years after 2010. #### b. Predicting with Linear Model Use your **linear** model to predict in which year the number of homes sold will reach (or did reach) 5000 homes. State the year. #### c. Exponential Model Formulation Write an **exponential** model \( n(t) = n_0 e^{rt} \) for the number of homes sold \( t \) years after 2010. *Round the value of \( r \) to 5 decimal places in your model.* #### d. Predicting with Exponential Model Use your **exponential** model to predict in which year the number of homes sold will reach (or did reach) 5000 homes. State the year. --- By analyzing the given data, you will develop both linear and exponential models to understand and predict the trajectory of home sales over time, showcasing different modeling techniques and prediction scenarios in real estate analytics.
Transcribed Image Text:### Real Estate Sales Analysis and Model Predictions The table below lists the number of homes sold by a real estate company in 2010 and 2015. Let \( t \) = the number of years after 2010 and \( n(t) \) = the number of homes sold \( t \) years after 2010. #### Table: Homes Sold by Year | Years after 2010, \( t \) | Number of homes sold, \( n(t) \) | |---------------------------|----------------------------------| | 0 | 200 | | 5 | 645 | --- #### a. Linear Model Formulation Write a **linear** model \( n(t) = mt + b \) for the number of homes sold \( t \) years after 2010. #### b. Predicting with Linear Model Use your **linear** model to predict in which year the number of homes sold will reach (or did reach) 5000 homes. State the year. #### c. Exponential Model Formulation Write an **exponential** model \( n(t) = n_0 e^{rt} \) for the number of homes sold \( t \) years after 2010. *Round the value of \( r \) to 5 decimal places in your model.* #### d. Predicting with Exponential Model Use your **exponential** model to predict in which year the number of homes sold will reach (or did reach) 5000 homes. State the year. --- By analyzing the given data, you will develop both linear and exponential models to understand and predict the trajectory of home sales over time, showcasing different modeling techniques and prediction scenarios in real estate analytics.
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