Exponential Functions y = a(b) x

Exponential Growth This graph shows exponential growth since the graph is increasing as it goes from left to right. Examples of exponential growth: y = 3(2) x a = 3 and b = 2

Exponential Decay This graph shows exponential decay since the graph is decreasing as it moves from left to right.

Experiment Click on the link below to experiment with a graph. Determine if the graphs are exponential growth or decay. Graphs of exponential functions Click on the role of a and b on the left of the screen to open applet. Change the value of b and leave a the same.

Graph Questions 1.What values of b make the graph exponential growth? 2. What values of b make the graph exponential decay? Answer: When b is between 0 and 1 0 < b < 1 Answer: When b > 1

Graph the equation y = 3(2 x ) 3 is the y-intercept Graph the equation y = 4(.75 x ) 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

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

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( ) 27 A = C(1 - r) t Step 4: Solve (1-.02)^(27)Type this into your calculator:= farms in 2010