Properties of Exponents
Exponential Functions
Percent Growth/Decay Problems
Geometric Sequences
Transformations of Exponential Functions (Shifts)
100
Simplify:
(4x^4)^5
1024x^20
100
Write an exponential function that has a growth factor of 2 and an initial value of 11.
y=11(2)^x
100
What percent change is modeled by this function?
y=19(1.4)^x
40% increase
100
Which sequence is GEOMETRIC
Sequence 1: 3, 6, 9, 12
Sequence 2: 8, 16, 32, 64
Sequence 2
100
What shift (number and direction) is indicated by the function:
f(x)=5^x-3
Down 3
200
Simplify using only positive exponents:
(4xy^5)/(16x^2y)
(y^4)/(4x)
200
Write the equation to model the values in the table:
y=81(1/3)^x
200
What percent change is modeled by this function?
g(x)=91(0.75)^x
25% decrease
200
What is the common ratio of this geometric sequence:
16, 24, 36, 54
r=3/2
200
What type of shifts are indicated by the function:
g(x)=3(.33)^(x-5)+1
5 right
1 up
300
Determine the value of n that will make the following true:
(x^n)/x^2=x^5
n=7
300
Write the equation of the function in this graph.
y=4(3/2)^x
300
Mr. Bader is 68 inches tall. He starts taking medicine to make him grow 2.5% taller each week. Write an equation, H(w), to model Mr. Bader's height, in inches, after w weeks.
H(w)=68(1.025)^w
300
Write the first 3 terms of a geometric sequence with a common ratio of 1/4 and
a_1=192
a_1=192;a_2=48;a_3=12
300
Write an equation that shifts the function below up 5 units.
f(x)=2(7)^x
g(x)=2(7)^x+5
400
Which of the following expressions is NOT equivalent to the others?
a)4^-2 ;b)1/16;c)-16;d)(4^4)/4^6
c)-16
400
Margo manages to acquire a magical maroon flower. The flower is 4cm long when she acquires it. The flower triples in length every minute. How long will the flower be, in cm, 15 minutes after she got it?
57,395,628 cm
400
Rehm pool has 200,000 gallons of water at 6:00 am. Due to the intense heat, the water is evaporating so that 11% of the water is evaporating every hour. How many gallons of water will be left at noon? (Round to the nearest whole number.)
99396 gallon
400
Write an explicit formula for the geometric sequence where the common ratio is 7 and
a_1=9
a_n=9(7)^(n-1)
400
If
f(x)=4(3)^x
write the equation for g(x) which is f(x) shifted left 4 and down 2.
g(x)=4(3)^(x+4)-2
500
What value of x makes this equation true?
(5^x)^3=5^x*5^10
x=5
500
An exponential function contains the points (0, 10) and (2, 490). Write the function.
f(x)=10(7)^x
500
Dr. Dufenshmirtz uses a super shrinking ray on Perry the Platypus. Perry initially weighs 150 kg. After one minute, he weighs 105 kg. What percent of weight is he losing each minute?
30%
500
Find the the 9th term in a geometric sequence in which
a_1=300; a_2=900
1968300
a_9=1968300
500
Write an equation for h(x), a transformation of f(x)
h(x)=2^(x-2)