Key Features
Exponential Functions
Graphing Exponential Functions
Exponential Growth and Decay
Geometric Sequences
100
Tell whether this graph is increasing or decreasing
y = 1/3(4)^x
What is
increasing
?
100
This is what the "a" and "b" values are in
a(b)^x
What is the y-intercept (starting value) and constant multiplier (pattern)?
100
Sketch a graph of exponential growth. What is special about "b" when it’s growth?
What is b > 1 ?
100
A savings account earns 4% interest per year. If Josiah puts 500 dollars in now, this is how much will he have after 5 years
What is $608.33?
100
Tell whether the following sequence is arithmetic, geometric, or neither. Give the common difference or common ratio if applicable.
2, 15, 112.5, 843.75, 6328.125, 47460.9375
What is Geometric and r=7.5?
200
Find the horizontal asymptote
y = 3(1/4)^x
What is
y = 0
?
200
This is the formula for exponential functions.
What is
a(b)^x
?
200
The graph of an exponential function will always cross the x - axis. True or false, explain your answer.
What is
false
?
200
The population of a small town is decreasing at a rate of 2% per year. in 1970 the population was 25,000. This is what the approximate population would be in the year 2020.
What is 9104?
200
Give the first 5 terms of the sequence given this recursive formula:
an = 0.5(an-1); a1 = 48
What is
48, 24, 12, 6, 3 ?
300
Give the y-intercept written as an ordered pair
f(x) = 2(3)^x - 3
What is
(0,-1)
?
300
These ordered pairs represent an exponential function; (-1, .5),(0,3),(1,18),(2,108). True or false, explain your answer.
What is true, there is a common ratio (6).
300
Sketch the graph of the following equation. Label the y-intercept in your graph.
y = 2^x
300
The number of students in the book club is increasing at a rate of 15% per year and they started with 9 students. How much would they have after 7 years?
What is ~24 students?
300
Find the 15th term of the sequence given this explicit formula:
an = 0.25(3)n-1
What is
1,195,742.25 ?
400
Give the domain and the range of the function
f(x) = 2^x
What are
(-inf, inf) and (0, inf) ?
400
This is the answer when f(x) = 10(5)^x is evaluated for f(3).
What is 1250?
400
Sketch the graph of the following equation. Label the y-intercept in your graph.
y = 4(1/2)^x
400
Fluorine-20 has a half-life of 11 seconds. This is the amount of fluorine-20 left from a 50 gram sample after 44 seconds.
What is 3.125 grams?
400
Give the explicit formula of the sequence represented by the given points:
(1, -64), (2, -16), (3, -4), (4, -1), (5, -1/4)
What is
an = -64(1/4)n-1
500
Give the interval when this graph is positive
f(x) = 2(1/2)^x - 4
What is
(-inf, -1)
?
500
The graph of an exponential function, V, passes through the points (0, 2) and (3, 128) as shown on the graph below. Write an equation for the function V(x).
What is
V(x) = 2(4)^x
500
Find the equation that models the following table.
What is
y = 3(2)^x
500
Ansley deposited $1000 into an account compounded quarterly at an annual 12% interest rate. How much is in her account after 20 years?
What is
$10,640.89
500
In the first week of summer, Marley earned $0.05. In the second week she earned $0.15. In the third week she earned $0.45. How much did Marley earn in the 11th week of summer?
What is
$2,952.45 ?