1. Exponential Functions y = a(b) x

6. Graph the equation y = 3(2 x ) Graph the equation y = 4(.75 x ) 3 is the y-intercept 4 is the y-intercept Notice that each number in the y column is being multiplied by .75 or 3/4 2 is the rate of change notice the 3,6,12,24,48… each number is multiplied by 2

7. Exponential Growth Equation Exponential Decay Equation A = C(1 + r) t A = C(1 + r) t A = ending amount C = starting amount r = rate as a decimal t = time

8. In 1983, there were 102,000 farms in Minnesota. This number drops by 2% per year. Write an exponential function to model the farm population of Minnesota and use that model to predict the number of farms in the year 2010 assuming the number continues to decline at the same rate. Step 1: Determine exponential growth or decay Since the number of farms have drops, we will use decay. Step 2: Identify the variables A = C = r = t = Unknown 102,000 2% = .02 as a decimal 2010 – 1983 = 27 years Step 3: Write an equation A = C(1 - r) t A = 102,000 ( 1 - .02) 27 A = C(1 - r) t Step 4: Solve 102000(1-.02)^(27) Type this into your calculator: = 59116 farms in 2010