4.1-4.5 Jeopardy

Graphing

100

What is the domain and range of f(x) = 2^x?

D: (-∞, ∞)
R: (0, ∞)

200

What is the asymptote of g(x)=log⁡₃(-x-5)?

VA: x=-5

300

For the function f(x)=2^x−2. What transformation occurred? What is f(0)?

Shifted down 2 units.

400

Compare the growth rate of f(x)=2^x and g(x)=3^x. Which one grows faster and why?

3^x grows faster because its base (3) is larger than 2, leading to a steeper exponential curve.

500

The function f(x) = -log₂(-x+5). State all the transformations, the asymptote, the domain, and the range.

Reflection across the y-axis

Horizontal shift right by 5

Reflection across the x-axis 

Vertical Asymptote: x=5

Domain: (−∞,5)

Range: (−∞,∞)

Exponential Equations

100

Solve for x: 2^x=16

4

200

Solve for x: 5^x+1=125

2

300

Solve 3^2x+1=27^x-1

4

400

Solve 5^2x+1 = 17

0.3805

500

Solve for x: e^2x + 7e^x - 8 = 0

0

Logarithmic Properties

100

Simplify: log⁡₃(9)

2

200

Rewrite in exponential form: log⁡₅(25)=2

5²=25

300

Expand: log⁡₂(4x³/y²)

(log₂(4)+3log₂(x))−2log₂(y)

400

Condense: log⁡5(x)+1/2log⁡₅(y)−log⁡₅(z)

log₅((xy^1/2)/z)

500

Find the numerical value of the log expression.

log⁡a=−1              log⁡b=12                 log⁡c=−3

30

Logarithmic Equations

100

Solve log⁡₂(x)=5

32

200

Solve ln⁡(x)=3

e³ or 20.09

300

Solve for x: log⁡₆(8x)−3log⁡₆(5)=0

125/8

400

Solve log₄(3x²-3) - log₄(x+1) = 1

7/3

500

Solve for x: 4ln(5x+3)−11= 13

(e⁶-3)/5

Compound Interest & Applications

100

What is the formula for compound interest with annual compounding?

A = P(1+r/n)^n*t

200

If you invest $1,000 at 5% annual interest compounded yearly, what is the balance after 2 years?

$1102.50

300

An element with a mass of 600 grams decays by 29.5% per minute. To the nearest minute, how long will it be until there are 2 grams of the element remaining?

16

400

Hassan is going to invest in an account paying an interest rate of 2.3% compounded continuously. How much would Hassan need to invest, to the nearest ten dollars, for the value of the account to reach $1,130 in 8 years?

940

500

Noah invested $8,600 in an account paying an interest rate of 2.4% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $10,900?

10