### Present Remotely

Send the link below via email or IM

• Invited audience members will follow you as you navigate and present
• People invited to a presentation do not need a Prezi account
• This link expires 10 minutes after you close the presentation

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

You can change this under Settings & Account at any time.

# Exponential Functions

Standard form, y-intercept, growth, decay, rate & percent of change, initial value
by

## Tracy Cottrell

on 9 May 2011

Report abuse

#### Transcript of Exponential Functions

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:
\$363.65

\$6517.36 A:
664 deer

244 deer x y 0
1
2
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:
135 rabbits

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
a=.4413415011
b=1.899316497
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?
Full transcript