6-3 Exponential Functions
What is the equation for an exponential function?
f(x)=a(b)x
An element with mass 490 grams decays by 18% per minute. Set up an exponential function, f(x), to represent this scenario.
f(x)= 490(0.82)x
What is the difference between arithmetic and geometric sequences?
Arithmetic has a common difference (adding), while geometric has a common ratio (multiplying).
Which direction does "x-3" shift the graph?
Right
Where do you find the initial amount of an exponential function on a graph or table?
Where x=0, or the y-intercept
What is the domain of f(x)=3(2)x?
all real numbers
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=9200(1.018)x
Growth; 1.8%
The explicit formula for geometric sequences is an=a1(r)n-1. What do a1 and r represent?
a1=1st term and r=constant ratio
Describe how g(x)=2x-4 changed from f(x)=2x
What is the most helpful tool in math class? (other than your brain, obviously)
Calculator
What is the range of f(x)=3(2)x?
y>0
A town has a population of 12000 and grows at 3.5% every year. What will be the population after 7 years, to the nearest whole number?
15,267 people
What's the common ratio for the following sequence:
5, 25, 125, 625
r=5
Describe how g(x)=2x-4 changed from f(x)=2x
Right 4
Come up with an example of something that GROWS at an exponential rate.
Answers will vary
What is the y-intercept of f(x)=3(2)x?
(0,3)
A town has a population of 14000 and grows at 3.5% every year. After how many years will the population reach 20,000?
After 10 years
Does the following sequence have a common difference or a common ratio? Is it a geometric sequence?
1.5, 3, 6, 12, 24
Common ratio; yes, it's a geometric sequence
Describe how g(x)=2x+1 -6 changed from f(x)=2x
Left 1 and down 6
Come up with an example of something that DECAYS at an exponential rate.
Answers will vary
Create a table of x and y values for the following exponential function: f(x)= 2(3)x
Use x values 0-3**
x: 0, 1, 2, 3
y: 2, 6, 18, 46
Johnny Chestnut competes in Nathan's Famous International Hot Dog Eating Contest. He starts off strong, but his hot dog intake decreases at a rate of 10% every minute. Sketch a graph of this and circle where the graph is decreasing more quickly.
Graphs should look like a backwards j and the steep section should be circled.
Write the explicit formula for the following geometric sequence:
416, 104, 26, 6.5, 1.625
an=416(1/4)n-1
Write a function, k(x), that has been shifted up 3 and left 5 from f(x)= 4x
k(x)= 4x+5+3
Come up with 5 terms in a geometric sequence that has a common ratio of 1/2 and its first term is 600
600, 300, 150, 75, 37.5