Exponential Functions and House Values

The video tutorial explains how to calculate the annual growth rate of a house's value using exponential growth. Starting with a house purchased for $110,000 in 1995 and valued at $162,000 in 2008, the tutorial demonstrates how to model this growth with an exponential function. It calculates the annual growth rate as 3.02% and predicts the house's value in 2012 to be approximately $182,414, assuming the same growth rate continues. The tutorial also highlights the limitations of such models, noting that real-world values can fluctuate.

What is the initial value of the house in 1995?

• $162,000

• $182,414

• $110,000

• $100,000

What is the base year used in the exponential function model?

• 2008

• 1995

• 2000

• 2012

What is the formula used to calculate the value of the house over time?

• F(T) = A^T x B

• F(T) = A x T^B

• F(T) = A x B^T

• F(T) = A + B^T

How do you solve for the base 'B' in the exponential function?

• Subtract 110,000 from both sides

• Raise both sides to the reciprocal power of 13

• Multiply both sides by 110,000

• Divide both sides by 162,000

What is the annual growth rate from 1995 to 2008 expressed as a percentage?

• 4.02%

• 3.02%

• 2.02%

• 5.02%

What is the value of the house predicted to be in 2012?

• $162,000

• $182,414

• $200,000

• $150,000

What is the value of 'R' in the exponential function?

• 0.0302

• 0.0202

• 0.0402

• 0.0502

What is the significance of the base 'B' in the exponential function?

• It is the time in years

• It is equal to 1 + R

• It is the growth rate expressed as a decimal

• It represents the initial value

What is a limitation of using the exponential growth model for predicting house prices?

• It assumes constant growth

• It requires a base year

• It uses a complex formula

• It only applies to houses

Why might the actual house value differ from the predicted value in 2012?

• The model uses incorrect initial values

• The model assumes prices always increase

• The model is only for short-term predictions

• The model does not account for inflation