Logarithmic Applications: Real-Life Exponential Challenges

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

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how long will it take for the population to reach 8000? (Use the formula N = N0 * 2^(t/T))

• 12 hours

• 24 hours

• 15 hours

• 6 hours

A sound level is measured at 80 decibels. What is the intensity of the sound in watts per square meter? (Use the formula L = 10 * log(I/I0) where I0 = 10^-12 W/m^2)

• 0.001 W/m^2

• 0.01 W/m^2

• 0.0001 W/m^2

• 0.1 W/m^2

The half-life of a radioactive substance is 5 years. If you start with 100 grams, how much will remain after 15 years? (Use the formula A = A0 * (1/2)^(t/T))

• 50 grams

• 25 grams

• 12.5 grams

• 5 grams

A car's value depreciates by 20% each year. If the car was originally worth $20,000, what will its value be after 3 years? (Use the formula V = P(1 - r)^t)

• $12,000

• $10,240

• $8,000

• $15,360

A bank offers an interest rate of 5% compounded annually. If you invest $1000, how long will it take for your investment to double? (Use the formula A = P(1 + r)^t)

• 25 years

• 10 years

• 20 years

• Approximately 14.21 years

The Richter scale measures the magnitude of earthquakes logarithmically. If an earthquake measures 6.0 on the Richter scale, how many times more intense is it than one that measures 4.0? (Use the formula I = 10^(M1 - M2))

• 200

• 100

• 50

• 10

A certain species of fish grows exponentially. If the population is currently 200 and grows at a rate of 10% per year, how long will it take to reach 500 fish? (Use the formula P = P0 * e^(rt))

• Approximately 9.21 years

• Approximately 20 years

• Approximately 15 years

• Approximately 5 years

A phone company claims that their battery lasts 2 hours longer than a competitor's. If the competitor's battery lasts 5 hours, how long does the company's battery last? (Use the formula for exponential growth)

• 4 hours

• 8 hours

• 6 hours

• 7 hours

A tree's height can be modeled by the equation h = 2 * log(t + 1), where h is the height in meters and t is the time in years. What will be the height of the tree after 4 years?

• 1.398 meters

• 0.800 meters

• 2.500 meters

• 1.200 meters