Logarithmic Applications: Solve and Convert Forms

A scientist measures the intensity of an earthquake using the Richter scale, which is logarithmic. If an earthquake has a magnitude of 6.0, what is the intensity of the earthquake in relation to a reference intensity of 1.0?

• 10000

• 100000

• 1000

• 1000000

The population of a city is modeled by the equation P = 1000e^(0.03t), where P is the population and t is the time in years. If the population reaches 2000, how many years will it take? Use logarithms to solve for t.

• 18.7

• 15.5

• 23.1

• 30.2

A sound level of 80 decibels is considered loud. If the sound intensity level is given by the formula L = 10 log(I/I0), where I0 is the reference intensity, what is the intensity I if L = 80?

• 1e-3 W/m^2

• 1e-4 W/m^2

• 1e-5 W/m^2

• 1e-6 W/m^2

A bank offers an interest rate of 5% compounded annually. If you want to know how long it will take for your investment to double, which logarithmic property can you use to find the time?

• Use the property of logarithms: log(a/b) = log(a) - log(b).

• Use the property of logarithms: log(a^b) = b*log(a).

• Use the property of logarithms: log(a+b) = log(a) + log(b).

• Use the property of logarithms: log(a^b) = log(a) + b.

The pH level of a solution is calculated using the formula pH = -log[H+]. If the concentration of hydrogen ions [H+] is 0.001 M, what is the pH of the solution?

• 2

• 4

• 5

• 3

A certain bacteria population doubles every 3 hours. If you start with 500 bacteria, how many will there be after 12 hours? Use logarithms to express your answer in terms of the initial population and the growth rate.

• 4000

• 2000

• 16000

• 8000

The formula for the half-life of a substance is t = (ln(2)/k), where k is the decay constant. If a substance has a decay constant of 0.1, what is its half-life?

• 10.00

• 3.47

• 6.93

• 5.00

A car's value depreciates according to the formula V = V0e^(-kt). If the initial value of the car is $20,000 and it depreciates at a rate of 15% per year, how long will it take for the car's value to drop below $10,000?

• 4.62 years

• 3.25 years

• 5.10 years

• 6.75 years

In a certain experiment, the amount of a radioactive substance remaining after t years is given by A = A0e^(-rt). If A0 is 100 grams and r is 0.05, how long will it take for the amount to reduce to 25 grams?

• 15.00 years

• 27.63 years

• 50.00 years

• 35.50 years

The formula for calculating the time it takes for an investment to grow to a certain amount is A = Pe^(rt). If you want to find out how long it will take for an investment of $1,000 to grow to $2,000 at an interest rate of 4%, how would you set up the equation using logarithms?

• t = ln(3) / 0.04

• t = 1000 * e^(0.04)

• t = ln(2) / 1000

• t = ln(2) / 0.04