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WorksheetsLogarithmic Applications: Solve and Convert Forms
Total questions: 10
Worksheet time: 5mins
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
