Exponential Growth:
• A pattern of change that increases over time
• it involves multiplication
• Each value is multiplied by the previous value by a constant factor which is called the growth factor
• How is this different from linear equations?
Ë Linear you add/sub by a constant value
• Exponential graphs start increasing slowly at first and then quickly; they form a curve
• How is this different from linear graphs?
Ë Linear graphs grow by a constant rate and are a straight line
Exponential Growth Equations: y = a(b)x
a = the starting amount; it also is the y-intercept
b = the growth factor
x = the time interval such as hours, days, years
Ë These equations differ from linear since the x becomes the exponent
Ë Investigation 1.2 the equation is y=2x
Ë Investigation 1.2 the equation is y=2(x-1)
Ë Investigation 1.3 the equation arevy=2(x-1) y=3(x-1) y=4(x-1)
Ë The larger the growth factor, the larger the growth since you are multiplying by a larger number.
Exponential Decay:
• pattern of change that decreases over time
• each value is multiplied by the previous value by a constant factor which is called the decay factor;
• You can find it by dividing each successive y-value by the previous y-value
• How is this similar to exponential growth?
• 1 minus the % decrease as a rate (decimal) OR ask yourself what % is remaining?
• How is this different from exponential growth?
• y = a(b)x same equation but the decay factor will be <1 Why?
• The graph starts out decreasing slowly then decreases quickly
• How is this different from exponential growth?
• Will the graph ever go pass the x-intercept?
• Examples in real-life: carbon dating to find the age of an object/organism; decay of radioactive substances; populations of endangered species; turntable sales
