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$100 $100 $100 $100 $100
$200
$300
$400
$500
$200 $200 $200 $200
$300 $300 $300 $300
$400 $400 $400 $400
$500 $500$500 $500
Exponents Scientific Notation
Exponential Growth and Decay
Properties of exponents
Geometry Sequences
Exponents for $100
Simplify: 4-3
Answer
Back
4-3 = 1/43 = 1/64
Exponents for $200
Simplify: (0.023454)0
Answer
Back
(0.023454)0 = 1
Exponents for $300
Simplify: 3-2 * 40
Answer
3-2 * 40 = 1/32 * 1 = 1/9
Back
Exponents for $400
Simplify: 22/(3*2)-2
Answer
Back
22/(3*2)-2 = 4*(3*2)2 = 4* 62
= 4*36 = 144
Exponents for $500
Evaluate
(2x3)/(3-2y-5) for
x = -2 and y = 4
Answer(2x3)/(3-2y-5) for x = -2 and y = 4
=2x3*32y5 = 2*9 *x3y5 = 18x3y5
= 18(-2)3(4)5
= 18*-8*1024
= -147456
Back
Scientific Notation for $100
Write the following number in scientific Notation:
3,450,000
3,450,000 = 3.45 x 106
Answer
Back
Scientific Notation for $200
Write the following number in scientific Notation:
.000073
Answer
.000073 = 7.3 x 10-5
Back
Scientific Notation for $300
Simplify. Write your answer in scientific notation:
(3.24 x 10-4)(5.2 x 10-2)
Answer(3.24 x 10-4)(5.2 x 10-2)
= 3.24*5.2 x 10-4 * 10-2
= 16.848 x 10-6
= 1.6848 x 10-5
Back
Scientific Notation for $400
Simplify. Write your answer in scientific notation:
(7.1 x 10-2)(2.3 x 104)
(7.1 x 10-2)(2.3 x 104)= 7.1*2.3 x 10-2 * 104
= 16.33 x 102
= 1.633 x 103
Answer
Back
Scientific Notation for $500
Simplify. Write your answer in scientific notation:
((1.3 x 103)(9.1 x 1012))2
Answer((1.3 x 103)(9.1 x 1012))2
(1.32 x 106)(9.12 x 1024)= (1.3*9.1)2 x 106 * 1024
= 139.9489 x 1030
= 1.399489 x 1032
Back
Properties of Exponents for $100
Simplify:
2x-1 * 3x5
Answer
2x-1 * 3x5 = 2*3*x-1+5 = 6x4
Back
Properties of Exponents for $200
Simplify:
(3x-3)/(9x4)
Answer
Back
(3x-3)/(9x4) = (3/9)*x-3 – 4 = (1/3)x-7 = 1/(3x7)
Properties of Exponents for $300
Simplify:
(x-3x5)/(x2y0)
(x-3x5)/(x2y0)
= (x-3+5)/(x2*1)
= x2/x2 = 1
Answer
Back
Properties of Exponents for $400
Simplify:
(y-7y3)-1
Answer
(y-7y3)-1 = (y-7+3)-1 = (y-4)-1
= y4
Back
Properties of Exponents for $500
Simplify:
(9x-2y5)2 * (3y2x-1)-3
Answer
(9x-2y5)2 * (3y2x-1)-3
= (92x-2*2y5*2)2 * (3-3y2*-3x-1*-3)-3
= (81x-4y10) * ((1/27)y-6x3)= (81/27)(x-4x3)(y10y-6)
= (3y4)/x
Back
Geometric Sequences for $100
Find the next three terms in the following geometric sequence:
3, 9, 27, 81, …
AnswerThe common ratio is 3, so the
next three terms are:
81*3 = 243
243*3 = 729
729*3 = 2187
243, 729, 2187Back
Geometric Sequences for $200
Write the formula for finding the nth term of a geometric sequence
A(n) = a1 * (r)n-1
Where:n is the nth terma1 is the first termr is the common ratio
Answer
Back
Geometric Sequences for $300
Find the 8th, 11th, and 13th terms in the following geometric sequence:
A(n) = 4(3)n-1
AnswerA(n) = 4(3)n-1
A(8) = 4(3)8-1 = 4(3)7 = 8,748
A(11) = 4(3)11-1 = 4(3)10 = 236,196
A(13) = 4(3)13-1 = 4(3)12 = 2,125,764
Back
Geometric Sequences for $400
Is the following sequence geometric, arithmetic, or neither? WHY?
4, 8, 12, 16, ….,
AnswerThe sequence is arithmetic because the
next term is found by adding 4 to the previous term. A geometric sequence would progress by multiplying, not adding.
Back
Geometric Sequences for $500
What is the difference between the equation for geometric sequences and the equation for exponential growth or decay?
Answer
The equation for a geometric sequence is to the power of n-1, while exponential growth and decay is to the power of x, not x-1.
Geometric sequence: A(n) = a1 * (r)n-1
Exponential growth/decay: y = a * (b)x
Back
Exponential Growth and Decay
for $100
Is the following equation exponential growth or exponential decay? Why?
A(n) = 5*(0.4)n
Answer
Exponential decay because r = 0.4 which means 0<r<1, thus telling you that it is exponential decay
Back
Exponential Growth and Decay
for $200
Is the following equation exponential growth or exponential decay? Why?
A(n) = 0.2*(7)n
Answer
Exponential growth because r = 7 which means r>1, thus telling you that it is exponential growth
Back
Exponential Growth and Decay
for $300
Write an equation to model the following situation (in other words, write an equation to find the number of balls left after n days)
Josh started with 200 balls, but loses half of them every day
Answer
A(n) = 200(0.5)n
Back
Exponential Growth and Decay
for $400
Joe invested $3200 in an account that earned 4% interest compounded every 3 months. Find the account balance after 5 years.
Answer
Back
y = a*bx where y = final balance, a = initial amount, b = interest rate and x = the number of times the interest is compounded. So,
a = 3200, b = 4% = 1 + .04 = 1.04 and x = 20 (4 per year for 5 years)
y = 3200(1.04)20 = $7011.59
Exponential Growth and Decay
for $500
Graph the following equation without using a calculator:
y = 3 *(1/2)x
Answer
Back
X Y
-1 6
0 3
1 3/2
2 3/4