Name _______________________________________________
Algebra II – Pd ___
Exponential Functions Review
Date _____________
Q3 Test 2
I – Solve and Check each of the following Exponential Equations
a) 3x + 2 = 9x
d) 4x = 23x + 1
g) 92x = 33x + 1
b) 8x – 2 = 22x
e) 55x + 10 = 25x + 2
h) 27x = 92x – 9
j) 42x + 4 = 82x
m) 100x + 1 = 1000x – 1
k) (3) = 27
n) 82x + 1 = 16x
p) 43x = 8x + 1
q) 4𝑥
1
s) 362𝑥−10 = (36)
𝑥−5
c) 2x + 3 = 64
f) 27x = 34x – 7
i) 9x + 5 = 812x + 1
1 𝑥+1
2 +4𝑥
1 𝑥
l) (2) = 4𝑥+3
o) 2x + 1 = 16
1
= 4−3
r) (16)
t) 272x + 4 = 9x – 4
𝑥−2
= 8𝑥+2
1 4𝑥
u) 42𝑥−7 = (64)
II – Graphing - For both graphs answer all the below questions
1) y = 4x for -2 < x < 2
a)
b)
c)
d)
e)
f)
g)
1 𝑥
2) f(x) = (2) for -3 < x < 3
Make the table for and graph the given exponential function. Which Quadrants?
Write the equation of the given graph when reflected in the y-axis. Which Quadrants?
Write the equation of the given graph when reflected in the x-axis. Which Quadrants?
What is the Range?
What is the Domain?
Is this a function? If so, is it one-to-one?
What is the y-intercept?
III – Describe the shifts of y = 2x
a) y = 2x – 4
d) y = 2x – 5
b) y = 2x + 3
e) y = 2x + 3 – 6
c) y = 2x + 4
f) y = 2x – 6 + 4
IV – Real World Applications
a) $2,000 is deposited into an account that pays 8% annual interest, compounded
monthly. What is the balance after 5 years?
b) $2,250 is deposited into an account that pays 6% annual interest, compounded
monthly. Find the balance after 1 year?
c) How much money must you deposit into an account that pays 6.25% interest,
compounded annually, to have a balance of $700 after 2 years?
d) How much money must you deposit into an account that pays 8% interest,
compounded quarterly, to have a balance of $3,585 after 11 years?
e) Rafferty-829, a new isotope of radium, decays according to the formula A = A0e-0.003861t
where A0 is the initial amount of the isotope and t is time in years. To the nearest
gram, how many grams will remain after 5 years if the initial amount is 500 grams?
How many grams will remain after 150 years?
Answer Key
I-
a) x = 2
d) x = -1
g) x = 1
j) x = 4
m) x = 5
b)
e)
h)
k)
n)
x=6
x = -2
x = -9
x = -4
3
x = −2
c) x = 3
f) x = 7
i) x = 1
l) x = -2
o) x = 3
p) x = 1
q) x = {-3, -1}
r) x = 7
s) x = 5
t) x = -5
u) x = 2
II – 1) a)
b)
c)
d)
e)
f)
g)
Quadrants I and II
x
4x y
-2 4-2 1/16
-1 4-1 ¼
0
40 1
1
41 4
2
42 16
2
1
2)
y = (¼)x Quadrants I and II
y = -(4x) Quadrants III and IV
Domain = {ℝ}
Range = {y > 0}
Yes it is a one-to-one function
The y-intercept is (0,1)
a)
Quadrants I and II
x
(½)x
f(x)
-3
-3
(½)
8
-2
-2
(½)
4
-1
-1
(½)
2
0
0
(½)
1
1
1
(½)
(½)
2
2
(½)
¼
3
3
(½)
1/8
b)
c)
d)
e)
f)
g)
f(x) = 2x Quadrants I and II
y = -(½x) Quadrants III and IV
Domain = {ℝ}
Range = {y > 0}
Yes it is a one-to-one function
The y-intercept is (0,1)
III – Shifts
a) down 4
d) right 5
b) up 3
e) left 3, down 6
c) left 4
f) right 6, up 4
IV – Real World Applications
a) $2,979.69
c) $620.07
e) 5 years – 490 grams
b) $2,388.78
d) $1,500.00
150 years – 280 grams