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Transcript of Exponential Functions
y=a b x . Standard Form: Growth: y=a(1+r) Decay: y=a(1-r) x x initial value rate of change (as a decimal) time intervals An exponential function describes something's (y) rapid growth OR rapid decay over a period of time (x). Is this graph an example of growth or decay? And this? total If this were a graph showing the population of bacteria over a span of 4 hours:
How many bacteria did I start with? Now how would I write the function? Population Time How are the bacteria increasing each hour? You deposit $300 into a savings account that has an interest rate of 8% compounded annually. How much money will you have in 2.5 years? In 40 years? y=( ) (1 ) ( ) . What the question is asking
Given time interval _______________________ = 2.5 years
1 year ___________ 40 years
1 year _________ x = = The population of deer in Yosemite National Park has declined due to the invading wolf population. If there were originally 700 deer in the park and they are decreasing at a rate of 10% every two years, how many deer will be left in 1 year? In 20 years? y=( ) (1 ) . ( ) A:
244 deer x y 0
3 What was the percent of change (rate as a percent) for the bacteria? A population of rabbits triples every 6 months. If there were 15 to begin with, how many rabbits will there be in 1 year? In 5 years? y=( ) ( ) . ( ) What is the % of change? A:
885,735 rabbits A:
200% Regression Curves! If you are given a table of values, you can find the regression curve from your calculator that tells you the function for that data set! STAT 1:Edit... ENTER STAT CALC 0: ExpReg ENTER ENTER y=a*b^x
r=.9979838936 (if you don't see the "r" value go to "Catalog," enter "DiagnosticOn" and then find ExpReg again) Correlation Coefficient: When multiplied by 100, this tells you that the curve found is 99.8% close to fitting your data. That's really close! Equation:
y=0.44(1.90) x Don't forget (7, 45.6)!! *THIS IS NOT YOUR RATE* Scientists use regression models to predict future events: Supercomputers more accurate than our calculators are used to find regression curves for data like this: How long will a plant grow if 10 cups of fertilizer are used? ? ? A:
269 inches What is this in feet?