8-1: Exponential Growth day 2 Objective CA 12: Students know the laws of fractional exponents, understanding exponential functions, and use these functions in problems involving exponential growth and decay.

Using Exponential Growth Models When a real-life quantity increases by a fixed percent each year (or other time period) the amount y of the quantity after t years can be modeled by Where a is the initial amount, and r is the percent increase expressed as decimal. The quantity 1+r is called the growth factor

Example 3: Modeling Exponential Growth In 1980 about 2,180,000 US workers worked at home. During the next ten years, the number of workers working at home increased by 5% per year. Write a Model giving the number of w (in millions) of workers working at home t years after 1930

Graph the model Use the graph to estimate the year when there were about 3.22 million workers who worked at home.

Compound Interest Consider the initial principal P deposited in an account that pays interest at an annual rate r (expressed as a decimal), compounded n times per year. The amount A in the account after t years can be modeled by this equation:

Example 4: Finding the Balance of an Account You deposit $1500 in an account that pays 6% annually. Find the balance of the account after 1 year if the interest is compounded: annually, semiannually, quarterly

8 – 1 day 2 Home work page – 48, 55, 62 –70