Logarithmic Expressions & Exponential Equations Quiz

A scientist measures the pH level of a solution, which is given by the formula pH = -log[H+]. If the concentration of hydrogen ions [H+] is 0.001 M, what is the pH of the solution?

• 1

• 7

• 3

• 10

A population of bacteria doubles every 3 hours. If the initial population is 500, how long will it take for the population to reach 8000? Use the exponential growth formula and solve for time.

• 20 hours

• 6 hours

• 12 hours

• 15 hours

The Richter scale measures the magnitude of earthquakes logarithmically. If an earthquake measures 5.0 on the Richter scale, how many times more powerful is it than an earthquake that measures 3.0?

• 200 times more powerful

• 50 times more powerful

• 10 times more powerful

• 100 times more powerful

A car's value depreciates at a rate of 15% per year. If the car was originally worth $20,000, what will its value be after 5 years? Use the exponential decay formula to find the answer.

• $10,500.50

• $5,000.00

• $8,874.37

• $12,000.00

A sound level of 60 decibels is considered normal conversation. If a sound level is measured at 80 decibels, how many times more intense is this sound compared to the 60 decibel level? Use the formula I = 10 log(I/I0).

• 100

• 200

• 50

• 10

The half-life of a certain radioactive substance is 10 years. If you start with 100 grams, how much will remain after 30 years? Solve using the exponential decay formula.

• 5 grams

• 50 grams

• 25 grams

• 12.5 grams

A bank offers an interest rate of 5% compounded annually. If you invest $1,000, how long will it take for your investment to double? Use the formula A = P(1 + r)^t and solve for t.

• Approximately 14.21 years

• 25 years

• 20 years

• 10 years

The formula for the intensity of an earthquake is I = I0 * 10^(M), where M is the magnitude. If an earthquake has a magnitude of 6.5, what is the intensity if I0 is 1?

• 3162277.66

• 5000000

• 2000000

• 1000000

A certain species of fish grows exponentially in a controlled environment. If the population is 200 and grows at a rate of 10% per week, how many fish will there be after 4 weeks? Use the exponential growth formula to find the answer.

• 298

• 400

• 320

• 250

A sound wave has an intensity of 0.0001 W/m². What is the sound level in decibels? Use the formula L = 10 log(I/I0) where I0 = 10^-12 W/m².

• 70 dB

• 80 dB

• 90 dB

• 100 dB