Chapter 3 Review

3.1 - Exponential Functions

100

If you have 2000 compounded monthly at a 5% annual rate, how much money will you have after 10 years?

$3,294.02

200

Plutonium has a half-life of 14 years and is modeled by the equation:

Q = 50(.5)^t/14

How much plutonium is left after 50 years?

4.21 grams.

300

You had invested $20,000 compounded continuously at an annual rate of 8% for 12 years while you were saving up for a house. If your new house requires a down payment of $50,000, how much would you have left over?

$2,233.93

400

NO CALCULATOR

Graph the following equation (show three points in a table) and draw your asymptote on your graph.

y = 2^x + 4

(0,5)

(1,6)

(2,8)

500

NO CALCULATOR

Graph the following equation (show three points in a table) and draw your asymptote on your graph.

y = 2^x+3 -2

(-3,-1)

(-2,0)

(-1,2)

(0,6)

3.2 - Logarithmic Functions

100

Rewrite this equation in logarithmic form:

3⁵ = 243

log₃243 = 5

200

NO CALCULATOR

Simplify:

log₂16

4

300

NO CALCULATOR

Simplify:

log₄(1/8)

-3/2

400

NO CALCULATOR

Graph the following equation (show three points in a table) and draw your asymptote on your graph.

y = 1 + log₂x

(1,1)

(2,2)

(4,3)

500

NO CALCULATOR

Graph the following equation (show three points in a table) and draw your asymptote on your graph.

y = -3 + log₂(x-1)

(2,3)

(3,4)

(5,5)

3.3 - Logarithmic Properties

100

NO CALCULATOR

Expand:

log₄7x

log₄7 + log₄x

200

NO CALCULATOR

Condense

3lnx + 2lny - 4lnz

(x³y²)/z⁴

300

NO CALCULATOR

5 ln e⁴

20

400

NO CALCULATOR

Evaluate

log₄2 + log₄16

5/2

500

NO CALCULATOR

Evaluate:

log₉2 - log₉54

-3/2

3.4 - Solving Equations

100

SOLVE

log₉(4 + x) = log₉(2x - 1)

x = 5

200

SOLVE

6^5x = 3000

x = .8937

300

SOLVE

log (x - 3) = 2

x = 103

400

SOLVE

6(8^-2-x) + 15 = 2601

x = -4.9172

500

SOLVE

2e^2x + e^x - 3 = 0

x = 0

3.5/3.6 - Non-Linear Models

100

Find the intensity of an earthquake that is measured on the Richter Scale as a R = 5.5.

R = log₁₀I/I_o

316,227.766

200

The average number N of words per minute that the students in a first grade class could read after t weeks of school is modeled by:

N = 62/(1 + 5.4e^-0.24t)

How many words did they students learn in 2 weeks?

About 14 words.

300

The average number N of words per minute that the students in a first grade class could read after t weeks of school is modeled by:

N = 62/(1 + 5.4e^-0.24t)

How long did it take the students to learn 40 words?

About 9.5 weeks.

400

The population P (in thousands) in Pittsburgh from 2000 to 2008 (with t=0 corresponding to 2000) can be modeled by the equation:

P = 333.68e^-0.0099t, where t is the year.

According to the model, what year will the population reach 290,000?

2014

500

Find an EXPONENTIAL model for the data below AND find out how much revenue was collected in 2015. (Use t = 1 for 2001)

Year - 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008

Revenue - 148.8, 177.8, 209.9, 230.3, 309.4, 433.2, 499.7, 581.9

y = 115.4671(1.2270)^x

$2483.86