7.1 Growth and Decay

An exponential equation has the general form 7.1 Exponential Growth and Decay An exponential equation has the general form y=abx

Given the general form: y=abx 7.1 Exponential Growth and Decay Given the general form: y=abx When b > 1, b is the growth factor When 0 < b < 1, b is the decay factor Such a situation is called  Exponential Growth. Such a situation is called  Exponential Decay.

Growth or Decay??? Growth Decay Growth Decay Growth Decay

7.1 Exponential Growth and Decay Many real world phenomena can be modeled by functions that describe how things grow or decay as time passes.  Examples of such phenomena include the studies of populations, bacteria, the AIDS virus, radioactive substances, electricity, temperatures and credit payments, to mention a few.

exponential growth exponential decay. Growth: Decay: 7.1 Exponential Growth and Decay Any quantity that grows or decays by a fixed percent at regular intervals is said to possess exponential growth  or  exponential decay. Growth: y = a(1+r)x Decay: y = a(1 – r)x a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) -> (rate = b-1) x = number of time intervals that have passed

Growth or Decay??? Rate = b-1 Growth Growth Rate: 0.2 or 20% Decay Decay Rate: 0.1 or 10% Growth Growth Rate: 0.54 or 54% Decay Decay Rate: 0.3 or 30% Growth Growth Rate: 1.0 or 100% Decay Decay Rate: 0.93 or 93%

A certain car depreciates about 15% each year. Example 1: A certain car depreciates about 15% each year. a. Write a function to model the depreciation in value for a car valued at $20,000. ____________________ b. Graph the function. c. Suppose the car was worth $20,000 in 2005. What is the first year that the value of this car will be worth less than half of that value? _________________

Example 2: Some real estate agents estimate that the value of a house could increase about 4% each year. a. Write a function to model the growth in value for a house valued at $100,000. ____________________ b. Graph the function. c. A house is valued at $100,000 in 2005. Predict the year its value will be at least $130,000. _________________

Example 3: Colleen’s station wagon is depreciating at a rate of 9% per year. She paid $24,500 for it in 2002. What will the car be worth in 2008 to the nearest hundred dollars? __________________________

Example 4: Kyle estimates that his business is growing at a rate of 5% per year. His profits in 2005 were $67,000. Estimate his profits for 2010 to the nearest hundred dollars. __________________________

Example 5: A parcel of land Jason bought in 2000 for $100,000 is appreciating in value at a rate of about 4% each year. a. Write a function to model the appreciation of the value of the land. ____________________ b. Graph the function. c. In what year will the land double its value? _________________