A2T Exponentials & Logs Jeopardy

Calculator-Free Exponents/Logs

100

The value of x if 2^x=64.

What is 6?

200

The value of x in the equation 3^2x=81.

What is 2?

300

The numerical value of log₅(125)?

What is 3?

400

log₄32, written as a fraction.

What is 5/2?

500

The simplified form of the expression:

log₂(8)+log₂(4)

What is 6?

Graphing Exponentials and Logs

100

The transformation applied to the graph of y=2^x to get the graph of y=2^x-3.

What is a shift 3 units to the right?

200

The transformations needed to graph y=-1*10^x-1 from the graph of y=10^x.

What is a reflection over the x-axis and a shift 1 unit right? (Both needed)

300

The y-intercept of the function y=3^x+2-4.

What is (0, 5)?

400

From the point (1,3) on the graph 3^x, this is the corresponding point on the graph -1*3^x+2

What is (1,-1)?

500

From the point (-1,2) on the graph of (1/2)^x, this is the corresponding point on the graph of (1/2)^x+1+2

What is (-2,4)?

Exponential Applications

100

A population of bacteria grows continuously with an initial population of 500 at a rate of 3% every hour. This is the population after 5 hours.

What is 581 bacteria?

200

A substance decays continuously at a rate of 5% every year. This is the amount of substance (rounded to the nearest tenth) left after 10 years from an initial sample of 200 grams.

What is 121.3 grams?

300

This is the amount in an account paying 6% interest per year with an initial investment of $1000 after 4 years. (Not compounded)

What is 1262.48?

400

A car worth $1500 depreciates at rate of 10% every year. This is the value of the car after 8 years.

What is 645.70?

500

The amount in an account after 3 years given:

- Compounded Quarterly

- Initial Investment of $5000

- Interest Rate 4% (per year)

What is $5634.13?

Log Properties

100

The expanded form of log_a(3xy)

What is log_a3+log_ax+log_ay?

200

The condensed form of 2log_b(4)+log_b(16)

What is log_b(256)?

300

The expanded form of the expression:

log_m[(x³y²)/(z)]

What is 3log_m(x)+2log_m(y)-log_m(z)?

400

The condensed form of log_k(2x)-log_k(5y)+log_k(10).

What is log_k(4x/y)?

500

The expanded form of log_p[(a²b³)/(c⁴d)]

What is 2log_p(a)+3log_p(b)-4log_p(c)-log_p(d)?

Solving Equations

100

The solution to the equation 2^x+1=16.

What is 3?

200

The solution to the equation log₃(x)+log₃(9)=2.

What is 1?

300

The solution to the equation:

5^2x=125.

What is 3/2 (or 1.5)?

400

The exact solution to the equation

e^x=5.

What is ln(5)?

500

The solution(s) of 2log(x)=log(3x-2).

What are 1 and 2?