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Build the Bouquet
Unit 4- Exponential Functions
𝑟(𝑥) = 5𝑥
Using the function above, state
the domain, range and
asymptote.
You deposit $1500 in an
account that pays 5% interest
compounded quarterly. Find
the balance after 6 years.
Determine the next 3 terms
of the geometric sequence
0.2, 1.2, 7.2, 43.2, . . .
The mice population is 25,000
and is decreasing by 20% each
year. Write a model for this
situation. What will be the mice
population after 3 years?
Given the exponential model
y = 200(.80)x, tell whether the
model represents exponential
growth or decay. Then, tell what
the growth/decay factor is and the
growth/decay percent.
Determine the 7th term in
the sequence defined by
𝑛−1
1
𝑔(𝑛) = 2 ·
2
Solve for n
813𝑛+2
4
=
3
243−𝑛
What is the explicit equation that
represents the sequence
1, 4, 16, 64, 256, . . .
Solve for x
2𝑥−1
25
3𝑥+2
= 125
Solve for x
2𝑥−1
3
1
≥
243
Given the function y=2x Write
the function g(x) that shows a
stretch of 4, a horizontal shift
of 2 units left and a vertical shift
of 6 units down.
In a geometric sequence if the
first term is 4, and the common
ratio is 6
a)Write the recursive formula
b)Write the explicit formula
𝑥
1
𝑘(𝑥) =
+5
3
Using the function above, state the
a)Asymptote
b) Interval of increase or decrease
c) End behavior
Describe the transformation
1
𝑓(𝑥) = −
2
𝑥−3
+2
𝑎𝑛 = 𝑎𝑛−1 ⋅ 3
𝑎1 = −3
Using the information above state
a)The common ratio
b)The first 5 terms of the sequence
Describe the differences in the
bases between an exponential
growth and exponential decay.
Kryptonite has a half-life of 2
years. There is 500 mg of
Kryptonite left on planet Krypton.
Superman cannot return home
until the Kryptonite is below 50 mg.
Can he return in 10 years? Explain
𝑚(𝑥) = 0.25𝑥 + 5
Use the function above to describe
a) Domain
b) Range
c)
Asymptote
d) x-intercept
e) y-intercept
f) End behavior
The number of mosquitos at Virginia
Beach has tripled every year since
2010. In 2010 there were 2500
mosquitos. How many mosquitoes
would you predict would be at the
beach in 2020?