Real-Life Logarithms: Conversions & Graphs for Grade 10

1. A scientist measures the intensity of an earthquake using the Richter scale, which is logarithmic. If an earthquake has a magnitude of 5.0, what is the intensity of the earthquake in terms of the base 10 logarithm?

• 10,000

• 50,000

• 100000

• 1,000,000

2. The population of a city is modeled by the function P(t) = 1000 * log(t + 1), where t is the number of years since 2000. How many years will it take for the population to reach 2000?

• 9

• 12

• 15

• 5

3. A sound level of 60 decibels is considered moderate. If the sound level is measured in decibels using the formula L = 10 * log(I/I0), where I0 is the reference intensity, what is the intensity I of the sound?

• 1e-6 W/m^2

• 1e-7 W/m^2

• 1e-4 W/m^2

• 1e-5 W/m^2

4. A bacteria culture doubles every 3 hours. If the initial amount of bacteria is 100, how many bacteria will there be after 12 hours? Use logarithms to express your answer in terms of time.

• 800

• 1600

• 2000

• 1200

5. 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?

• 1

• 5

• 7

• 3

6. A car's value depreciates according to the formula V(t) = V0 * e^(-kt), where V0 is the initial value, k is a constant, and t is time in years. If the car's value after 5 years is $10,000 and its initial value was $25,000, what is the value of k?

• 0.0950

• 0.0754

• 0.1323

• 0.2001

7. The half-life of a radioactive substance is 5 years. If you start with 80 grams, how much will remain after 15 years? Use logarithms to find your answer.

• 5 grams

• 10 grams

• 20 grams

• 40 grams

8. 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 logarithms to solve for the time.

• Approximately 14.21 years

• 10 years

• 20 years

• 25 years

9. The formula for the decay of a substance is N(t) = N0 * (1/2)^(t/T), where T is the half-life. If the half-life is 10 years and you start with 200 grams, how much will remain after 30 years?

• 10 grams

• 100 grams

• 25 grams

• 50 grams

10. A logarithmic function is graphed as y = log(x). Describe how the graph behaves as x approaches 0 and as x increases. What are the key features of this graph?

• The graph of y = log(x) approaches positive infinity as x approaches 0 and decreases slowly as x increases.

• The graph of y = log(x) remains constant at y = 0 for all values of x.

• The graph of y = log(x) increases rapidly and then levels off as x approaches 10.

• The graph of y = log(x) approaches negative infinity as x approaches 0 and increases slowly without bound as x increases.