Real-Life Logarithmic Applications and Properties Quiz

A scientist measures the pH level of a solution and finds it to be 3. What is the hydrogen ion concentration in moles per liter? (Use the formula pH = -log[H+])

• 0.1 moles per liter

• 0.0001 moles per liter

• 0.001 moles per liter

• 0.01 moles per liter

The population of a bacteria culture doubles every 3 hours. If the initial population is 500, how long will it take for the population to reach 8000? (Use logarithmic properties)

• 6 hours

• 15 hours

• 10 hours

• 12 hours

A sound engineer records a sound at 80 decibels. If the sound intensity increases to 90 decibels, how many times more intense is the sound? (Use the formula dB = 10 log(I/I0))

• 20

• 10

• 50

• 5

A car's value depreciates according to the formula V = P(1 - r)^t, where V is the value after t years, P is the initial price, r is the depreciation rate, and t is time. If a car is worth $15,000 after 5 years and the depreciation rate is 15%, what was its original price? (Convert to logarithmic form)

• 40000

• 33762.34

• 25000

• 18000

A bank offers an interest rate of 5% compounded annually. If you want to have $10,000 in the account after t years, how long will it take to reach that amount if you start with $5,000? (Use logarithms to solve for t)

• 5 years

• 14.2 years

• 10 years

• 20 years

The Richter scale measures the magnitude of earthquakes logarithmically. If an earthquake measures 6.0 on the Richter scale, how many times more powerful is it than one that measures 4.0? (Use the formula M = log(I/I0))

• 50

• 10

• 100

• 200

A certain radioactive substance has a half-life of 10 years. If you start with 80 grams, how much will remain after 30 years? (Use logarithmic properties to find the remaining amount)

• 40 grams

• 10 grams

• 20 grams

• 5 grams

A smartphone's battery discharges according to the formula B(t) = B0 e^(-kt), where B0 is the initial battery life, k is a constant, and t is time in hours. If the battery lasts 10 hours initially, how long will it take for the battery to drop to 25% of its original life? (Use logarithms to solve for t)

• 15 hours

• 30 hours

• 5 hours

• 20 hours

A population of fish in a lake is modeled by the equation P(t) = P0 e^(rt). If the population is 2000 fish now and is expected to grow to 5000 fish in 5 years, what is the growth rate r? (Convert to logarithmic form)

• r = ln(3) / 5

• r = ln(2.5) / 5

• r = ln(2) / 10

• r = ln(1.5) / 5

A music track has a frequency of 440 Hz. If the frequency is increased to 880 Hz, how many octaves has the frequency increased? (Use the formula n = log2(f2/f1))

• 3 octaves

• 1 octave

• 2 octaves

• 0.5 octaves