Characteristics of Exponential Functions
Identify the asymptote of the graph. (Question 1)
y = 3
What is the horizontal asymptote for the function f(x) = 6(4)x - 8? (Question 4)
y = k = -8
How does the "k" value transform the graph? Hint: There are two. (Not on Study Guide)
transforms the graph UP (+) or DOWN(-)
A culture of bacteria doubles every hour. If there are 1,000 bacteria at the beginning, how many bacteria will there be after 5 hours? (Question 12)
32,000 bacteria
What is the explicit formula for a Geometric Sequence? (Not on Study Guide)
an = a1(r)n-1
Identify the range of the graph. (Question 2)
(3, infinity)
Identify the exponential function given by the x & y table on Question 10.
A. y = 4x
How does the "h" value transform the graph? Hint: There are two. (Not on Study Guide)
transforms the graph RIGHT(-) or LEFT(+)
The population of a small town has established a growth rate of 5% per year. If the current population is 1500, and the growth rate remains steady, what will the population be in 8 years? Round answer to the nearest tenth. (Question 13)
~2,216 people
What value is missing in the third position of the geometric sequence below? (Question 19)
80
Use the equation f(x) = 10,000(5.25)t. Does this equation represent a growth or a decay? Why? (Question 11)
Growth, b>1
Write the function represented by the graph from Question 8. (assume a=1 & b=2)
y = 1(2)x + 3 or y = 2x + 3
How does the "a" value transform the graph? Hint: There are three. (Not on Study Guide)
transforms the graph by stretching (a>1) it or shrinking (a<1) and reflects it over the x-axis
A doctor prescribes 500 milligrams of medicine to treat an infection. Each hour following the initial dose, the concentration that remains in the body decreases by 5%. Write the function that models the situation. (Question 14)
y = 500(1 - .05)t
Find the geometric sequence with the ratio r= -3. (Question 17)
A. 1, -3, 9, -27,...
Determine the end behavior of the graph (Question 3):
as x approaches -infinity, f(x) approaches ___.
the asymptote, 3
Write the function represented by the graph from Question 9. (assume a=1 & b=2)
y = 1(2)x - 3 or y = 2x - 3
Describe the transformations of the parent function f(x) = 2x to the function g(x) = -2(2)x-1 + 3. (Question 6)
reflection over x-axis, stretch by 2, right 1, up 3
Adison invested $1500 into an account that earns 4% compounded quarterly. Create an exponential function to model this situation if has the account for 10 years. (Question 15)
y = 1500(1 + .04/4)4x10
or
y = 1500(1 + .04/4)40
In a geometric sequence the ratio of any term divided by the term before it is always the same.
32, 16, 8, 4, 2,...
What is the ratio in the geometric sequence shown above? (Question 20)
r = 1/2
Determine the end behavior of the graph (Question 3):
as x approaches infinity, f(x) approaches ___.
infinity
Sketch the graph of y = -2(1/2)x - 5. (Question 7) (Hint: Graph in Desmos, then on your Study Guide sheet).
Teacher check of sketch on Study Guide/graph in Desmos.
The parent function f(x) = 2x is translated left 5 units, and translated down 2 units to create g(x). Use the transformations described to write the NEW exponential function. (Question 5)
f(x) = 2x+5 - 2
Edwin decided to invest money in an account that earns 6% compounded semi-annually. If he initially deposited $550 into the account, how much will it be worth in 4 years? Round answer to the nearest hundredth. (Question 16)
y = ~$700 ($696.72 rounded up)
Write explicit formula for the sequence shown in the table from Question 18.