Exponential Growth
The general form of an exponential growth equation is this.
y=a(b)^x
The base of an exponential decay function is always between these two numbers.
0 and 1
The percent change factor for a 5% increase is this.
1.05
Is the rate of change in exponential functions constant or not constant?
The graph of y=2^x passes through this point on the y-axis.
(0, 1)
If a population doubles every year, what is the growth factor?
2
If a substance decreases by 20% each hour, what is the decay factor?
0.8
The percent change factor for a 30% decrease is this.
0.7
In y=2⋅4^x , what is the rate of change between x=0and x=1 ?
6
The graph of an exponential decay function approaches but never touches this line.
x-axis or y=0
In the equation y=5⋅3^x , what does the 5 represent?
the initial value
In y = 200(0.5)^x, what does the 0.5 represent?
the decay factor
If a quantity increases by r % per period, the growth factor is given by this expression.
1 + r/100
How does the rate of change in exponential functions compare to that in linear functions?
the rate of change increases or decreases multiplicatively in exponential functions, but is constant in linear functions
What is the y-intercept of y=4⋅0.5^x ?
4
If y=100⋅1.08^x , what is the percent increase per period?
8%
If y=300⋅0.9^x , what percent does the value decrease each period?
10%
If a quantity decreases by r % per period, the decay factor is given by this expression.
1 - r/100
Find the average rate of change of y=3⋅2^x from x=1 to x=3.
21/2
Describe the end behavior of y = 3^x as x increases
the graph increases rapidly and approaches infinity
A bacteria culture triples every hour. Write an equation for the population after xx hours if the initial population is 50.
y=50(3)^x
A car’s value depreciates by 12% per year. If it was worth $20,000 new, write an equation for its value after x years.
y = 20,000(0.88)^x
A population grows by 3% for 4 years. What is the total percent growth factor over 4 years?
1.03^4
Explain why the rate of change in y=a⋅b^x depends on both a and b .
because both the initial value and the growth/decay factor determine how quickly the function increases or decreases
Compare the graphs of y=2^x and y=2^-x
y = 2^-x is a reflection of y = 2^x over the y-axis.