Exponent Laws
Keeping your answer in positive exponents, simplify:
y^(3) * 7y^3
What is
7y^6
In exponential functions when b>1 this will cause an exponential growth or decay?
Exponential growth
When interest is compounded quarterly, what do we use as n?
n= 4
10^(x+1)=10^(3x-9)
x=5
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.
What is 5.25% as a decimal?
.0525
Keeping your answer in positive exponents, simplify:
4p^-3
What is
(4)/(p^3)
In exponential functions when 0<b<1 this will cause an exponential growth or decay?
Exponential decay
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.
15^(2x+5) = 15^(3x-14)
x=19
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
What is the name of this random sequence?
0,1,1,2,3,5,8,11,etc
Fibonnaci Sequence
Keeping your answer in positive exponents, simplify:
(x^(2)y^(5))^2
What is
x^(4)y^(10)
What is the function for exponential decay?
y=a(1-r)^t
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
3^(2x)=81^(x-1)
x=1/2
Write a formula for the following geometric series:
2,10,50,250,...
an=2(5)n
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?
530000(1.05)6
=$710,250 or =$710,251
Keeping your answer in positive exponents, simplify:
(-8mn^4)/(-7mn)
What is
8/(7n^3)
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
$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)
8^(3-2x)=512
x=0
Write a formula for the geometric sequence below:
5,-10,20,-40,80,...
An=5(-2)n-1
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?
f(x)=26400(.88)3.5
=$16,876 or =$16,877
Keeping your answer in positive exponents, simplify:
(3x^3)/y^-6
What is
3x^(3)y^(6)
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
$1500 at 5% interest rate compounded monthly. What will be the balance after 2 years?
=$1,657
25^(x-2)=125^(3x+1)
x= -1
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
Determine the amount of interest earned on a $2500 investment if it is invested at 5.25% annual interest compounded monthly for four years.
(read carefully)
The amount of interest earned is $582.78