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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


Write the following number in scientific Notation:

.000073

Answer

.000073 = 7.3 x 10-5

Back


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



(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



((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


Simplify:

(3x-3)/(9x4)

Answer

Back

(3x-3)/(9x4) = (3/9)*x-3 – 4 = (1/3)x-7 = 1/(3x7)


Simplify:

(x-3x5)/(x2y0)

(x-3x5)/(x2y0)

= (x-3+5)/(x2*1)

= x2/x2 = 1

Answer

Back


Simplify:

(y-7y3)-1

Answer

(y-7y3)-1 = (y-7+3)-1 = (y-4)-1

= y4

Back


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


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


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


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


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


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


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


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


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


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

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