Logarithm Ladder: Scaling New Heights in Algebra 2!

Exponential Rules

100

What is the value of 2⁰ ?

1

200

Simplify:

(3²)³

3⁶ or 729

300

Rewrite log_⁡b(x³) using properties of logarithms.

3 x log_b(x)

400

Simplify:

5^x+1÷5^x

5

500

Solve for x: 

3^2x−1=81

x=2

Simplification

100

Simplify:

log⁡₁₀(1000)

3

200

Expand:

log⁡(xy)

log(x) + log(y)

300

Simplify:

2^x+2/2^x

2² = 4

400

Solve for x: 

10^x=1000

x = 3

500

Simplify:

5^x+3/25^x

5^x+3/5^2x = 5^3-x

Compound Interest

100

What is the formula for compound interest?

A=P(1+r/n)^nt

200

If you invest $1,000 at 5% annual interest compounded yearly, how much will you have after 1 year?

$1,050

300

What is the difference between simple and compound interest?

Compound interest earns interest on the principal and previous interest; simple interest earns only on the principal.

400

How long will it take for $1,000 to double at 7% annual interest, compounded annually?

≈ 10.24 years

500

If you invest $500 at 6% interest, compounded monthly, for 10 years, what is the total?

about $909.29

Wages vs. Inflation

100

Define "inflation" in one sentence.

Inflation is the increase in prices of goods and services over time, reducing purchasing power.

200

If the average wage in 1980 was $15,000 and inflation caused the cost of living to double by 2020, what is the equivalent wage needed in 2020?

$30,000

300

If inflation averages 3% per year, approximately how many years will it take for prices to double?

About 24 years

400

In 2000, a Big Mac cost $2.50. If inflation averaged 2% annually, what would be its cost in 2025?

About $4.10

(2.50×(1.02)²⁵

500

In 2025, the minimum wage is $15/hour, but inflation-adjusted wages should be $20/hour. How much of a raise is needed to match inflation?

$5/hour

Trivia

100

If Shrek’s swamp has 7 layers like an onion and the number of layers doubles every year, how many layers will the swamp have in 3 years?

7⋅2³=56 layers

200

In Stranger Things, the Mind Flayer controls 64 Demodogs in Hawkins. If the population increases exponentially and doubles every 2 months, how many Demodogs will there be in 6 months?

64⋅2³=512 Demodogs

300

Wednesday Addams finds a secret message written in a clock puzzle. The clock strikes 13, representing 390 degrees. Convert this to radians in simplest form.

390×π/180=13π/6 radians

400

SpongeBob flips Krabby Patties at a rate of 3^t+1 patties per hour, where t is the number of hours into his shift. How many patties does he flip in 3 hours?

3³⁺¹ = 3⁴ =81 patties

500

Solve for x:

 3^2x−1 = 243

x=3