Geometric
Exponential Growth
Exponential Decay
Compound Interest
Exponent Laws
100
What is the difference between Arithmetic and Geometric Sequences?
Arithmetic has common difference and Geometric has common ratio.
Arithmetic uses addition/subtraction and Geometric uses multiplication/division.
100
If f(x)=a(1+r)x
Then what is the initial amount and growth rate?
initial amount=a
growth rate = r
100
If f(x)=a(1-r)x
Then what is the initial amount and decay rate?
initial amount = a
decay rate = r
100
When interest is compounded quarterly, what do we use as n?
n= 4
100
Keeping your answer in positive exponents, simplify:
y^(3) * 7y^3
What is
7y^6
200
Is the sequence below arithmetic or geometric? Explain your answer.
200, 100, 50, 25, 12.5, 6.25
Geometric with a common ratio of 1/2
200
In exponential functions when b>1 this will cause an exponential growth or decay?
Exponential growth
200
In exponential functions when 0<b<1 this will cause an exponential growth or decay?
Exponential decay
200
How do you turn 7% into a decimal?
What is the given decimal of 7%?
7/100= .07
or you move the decimal two places to the left of 7 to get .07.
200
Keeping your answer in positive exponents, simplify:
4p^-3
What is
(4)/(p^3)
300
Write a formula for the following geometric series:
2,10,50,250,...
an=2(5)n
300
Does the graph represent exponential growth or decay?
Exponential Growth
300
Does the graph represent exponential growth or decay?
Exponential Decay
300
Ms. Wiggins deposited $1,000 in a CD at a 7% interest compounded quarterly. How much will her CD be worth in 5 years?
Identify the P,r,n & t.
p=1,000
r=.07
n=4
t=5
300
Keeping your answer in positive exponents, simplify:
(x^(2)y^(5))^2
What is
x^(4)y^(10)
400
Write a formula for the geometric sequence below:
5,-10,20,-40,80,...
An=5(-2)n-1
400
What equation would represent the situation below?
Gina started with 14 frogs in 2004. Her frogs increase at a rate of 20% each year. How much frogs would she have in 2008?
y=14(1+0.2)4
400
What is the equation we can use to represent the situation below?
Marvin invested $1000 a stock that is going down each year by 0.5%. In 5 years, how much money would he have left?
y=1000(1-0.005)5
400
$950 at 6.5% for 8 years compounded annually. What is the exponential model (equation, not answer) that represents exponential growth?
A=P(1+r/n)nt
A=950(1+.065/1)1(8)
400
Keeping your answer in positive exponents, simplify:
(-8mn^4)/(-7mn)
What is
8/(7n^3)
500
Find A7 (the seventh term) in the sequence below.
1000, 100, 10, 1,...
An=1000(1/10)n-1
A7=1000(1/10)7-1=1000(1/10)6= 0.001
500
Annual sales of a fast food restaurant are $530,000 and increasing at a rate of 5%. What will the annual sales be in 6 years?
A=P(1+r)n
530000(1.05)6
=$710,250 or =$710,251
500
Ms. Wiggins purchased a car for 26,400 and every year it depreciates by 12%. What she expect the value of her car to be after 3.5 years?
A=P(1-r)n
f(x)=26400(.88)3.5
=$16,876 or =$16,877
500
$1500 at 5% interest rate compounded monthly. What will be the balance after 2 years?
=$1,657
500
Keeping your answer in positive exponents, simplify:
(3x^3)/y^-6
What is
3x^(3)y^(6)