Unit 5 - Exponents and Logarithms Test Review

Properties of Exponents

100

x² times x⁷

x⁹

200

y/y⁵

y^-4 which equals 1/y⁴​​​​

300

(4x⁴)²

16x⁸

400

(3 + x³)²

9 + 6x³ + x⁶

500

16^3/2

64, because 16^3/2 = (16^1/2)³ = 4³ = 64

Properties of Logarithms

100

log₁₀⁡100,000

5, because 10⁵ = 100,000

in other words, 10 x 10 x 10 x 10 x 10 = 100,000

200

log⁡ 5 + log 200

3, because log⁡ 5 + log 200 = log 1000

and 10³ = 1000

300

ln(1)

0, because e⁰ = 1

400

Solve the equation log₃⁡x=2

9. This equation can be rewritten as 3² = x

so x = 9

500

log₅ 100 - log₅ 4

2, because log₅ 100 - log₅ 4 = log₅ 25

and 5² = 25

Exponential growth and decay word problems

100

Jeffs retirement account has $350 in it and it accrues interest at a rate of 4% compounded annually. How much will be in the account after 10 years?

$518.09 roughly, 350(1 + 0.04)¹⁰

200

Gas is decreasing by 1% of its cost each week. If the current cost of gas is $4.00, what would it cost in 5 weeks?

$3.80, because 4(1 - 0.01)⁵ = 3.80

300

Each year, the price of starbucks has been going up 5%. If my current order currently costs $6.30, what was the cost of my order 7 years ago?

$4.48, because 6.30(1 + 0.05)^-7

400

I am a terrible friend and double the amount of money he owes me every year (100% interest essentially)

If he currently owes me $800, how much would he owe me in 5 years?

$25600, because 800(1 + 1.00)⁵ = 25600

500

The half-life of one radioactive element is 3 years, meaning 50% of its mass/atoms decay after that time.

If there is initially 100 grams of the element, how much would still exist of 24 years?

0.39 grams, because 100(1 - 0.50)⁸ = 0.39

Continuously compounded interest word problems

100

My evil credit card company starts charging me continuously compounded interest after I missed a payment. 

If I owe $490 and I do not make any payments for two years, how much would I owe at an APR of 25%?

807.87, because 490(e)^0.25*2 = 807.87

200

My evil credit card company starts charging me continuously compounded interest after I missed a payment. 

If I owe $1350 and I do not make any payments for eleven years, how much would I owe at an APR of 28%?

$51323.98, because 1350(e)^0.28*13

300

Continuously compounded interest at an APR of 5% is applied to an investment of $1000. How long does it take for the investment to reach $2718.28

20 years

2718.28 = 1000(e)^0.05t, so ln or log_e(2.71828) = 1

so 0.05t = 1 meaning t = 20

400

Continuously compounded interest at an APR of 4% is applied to an investment of $1000. How long does it take for the investment to reach $2000

Roughly 17.33 years

2000 = 1000(e)^0.04t so ln(2) = 0.6931

If 0.04t = 0.6931, then t = 17.33

500

Continuously compounded interest at an APR of 6% is applied to an investment of $5000. How long does it take for the investment to reach $7166.65

6 years

7166.65 = 1000(e)^0.06t, so ln or log_e(7.16665) = 0.36, so t = 6

Random Trivia

100

Which of these things have I not eaten today

A) Apple

B) Banana

C) Cookie

D) Waffle

B) Banana

200

What year is my car?

A) 2010

B) 2004

C) 2007

D) 2001

B) 2004

300

Name three states smaller than Maryland by land area

Hawaii, Massachusetts, Vermont, New Hampshire, New Jersey, Connecticut, Delaware, and Rhode Island

400

Which of these is the capital of California?

A) San Francisco

B) Los Angeles

C) San Diego

D) Sacramento

D) Sacramento

500

How far is it from home plate to first base in baseball?

90 feet