Applying Logarithms: Real-World Problem Solving for Grade 10

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?

• 7

• 3

• 10

• 1

The population of a certain city is modeled by the equation P(t) = P0 * e^(kt), where P0 is the initial population, k is a constant, and t is time in years. If the population doubles in 5 years, what is the value of k?

• 0.22314355131420976

• 0.06931471805599453

• 0.09531017980432593

• 0.13862943611198905

A sound intensity level is measured in decibels (dB) using the formula L = 10 * log(I/I0), where I is the intensity of the sound and I0 is the reference intensity. If a sound has an intensity of 1000 times the reference intensity, what is its sound level in decibels?

• 100 dB

• 50 dB

• 30 dB

• 10 dB

A bank offers an investment that grows according to the formula A = P(1 + r/n)^(nt). If you want to find out how long it will take for your investment to double, you can use logarithms. If the interest rate is 5% compounded annually, how many years will it take to double your investment?

• 5 years

• 10 years

• 14.21 years

• 20 years

The Richter scale measures the magnitude of earthquakes using the formula M = log(I/I0), where I is the intensity of the earthquake and I0 is a reference intensity. If an earthquake has an intensity of 1000 times the reference intensity, what is its magnitude on the Richter scale?

• 10

• 100

• 1

• 3

A certain bacteria population grows exponentially and can be modeled by the equation N(t) = N0 * e^(rt). If the population triples in 4 hours, what is the growth rate r?

• 0.1

• 0.5

• 0.75

• 0.2740686190612002

The half-life of a radioactive substance is the time it takes for half of the substance to decay. If the half-life is 10 years, how long will it take for 75% of the substance to decay? Use logarithms to find your answer.

• 15 years

• 5 years

• 30 years

• 20 years

A car's value depreciates according to the formula V = V0 * e^(-kt). If the car's value is half of its original value after 6 years, what is the value of k?

• 0.1155

• 0.0500

• 0.0753

• 0.2001

In a certain experiment, the amount of a substance decreases according to the formula A(t) = A0 * e^(-kt). If the substance decreases to 25% of its original amount in 8 hours, what is the decay constant k?

• 0.2500

• 0.1733

• 0.5000

• 0.1250

A photographer uses a logarithmic scale to measure the brightness of light. If a light source is 100 times brighter than a reference light source, what is the brightness level in logarithmic terms?

• 2

• 1

• 3

• 10