The Jeopardy

Basic Logs

100

What is ln(5)?

1.609

200

What is ln(271)?

5.602

300

What is ln(4^x)?

x ln(4)

400

What is ln(5^2x)?

2x ln(5)

500

What is the simplified version of ln(10) - ln(2)?

ln(5)

Fancy Logs

100

If 10^x = 50, what is x?

1.699

200

If 10^x+1 = 25, What is x?

0.398

300

What is ln(6^x+1)?

(x+1) ln(6)

400

What is ln(4^{x^4})?

x⁴ ln(4)

500

What is ln(2x³-4x²+5x-5)?

ln(x(2(x-2)x+5)-5)

Real World Applications

100

Julia bought a brand new car for $40,000 in 2020. The car depreciates at 10% a year. How many years until it is only worth $32,400?

v(t) = 40000 * 0.9^t

2 years

200

Since 1995, The daily cost of hospital care has increased by 4% per year. If the average was $968 per day in 1995, what is the cost of daily care in 2021?

$2,683

300

This model demonstrates the growth of honey production in ounces over time per month

h(t) = 5 * 1.09^t

What is the growth rate of honey production? in other words,

9%

400

A computer system is originally worth $12,000. It decreases at a rate of 4% per month. In how many months is it worth $7,350?

v(t) ​= 12000 * 0.96^t​​​

12 months

500

A scientist is trying to discover a cure for the common cold. She takes 40 common cold cells and discovers the cells are tripling every 30 minutes.

c(t) = 40 * 3^2t

How many cells will there be in 3 hours?

29160

My Cat Died

100

How long is a football field?

360 feet

200

How big is that poster in the back?

10 feet

300

How tall is Mr. P?

6' 2"

400

What grade do you need for F1 to be exempt from the final?

Above an 80

500

What brand of car does Mr. P drive?

Hyundai