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Pre-Calculus 12

Logs & Exponents: Applications Worksheet

1. a) Use logarithms to determine how long it would take for an investment of $3000 compounded annually at 12% to reach $10 000.

b) Calculate how many years it would take for the investment to double.

2. In 1994 a certain city in Saskatchewan has a population of 40 000 and was growing at a rate of 6.1% per year.

a) Write an exponential equation to represent the population as a function of time.

b) Assuming this rate continues, how long would it take for the city’s population to double?

c) Rewrite the equation in part a) as an exponential function with a base of 2 to represent doubling time.

3. The intensity (I) of light in fog can be modeled by the equation [pic], where d is the distance in meters away from the light source.

a) Use logarithms to determine the half-life for the intensity of light.

b) Rewrite the equation using a base of 0.5 to represent an exponential function that has a half-life.

4. The battery in a laptop computer loses 15% of its charge every hour. Assume the battery is fully charged.

a) Write an equation to represent the percentage P, as a function of the number of hours h, beginning when the battery was fully charged.

b) Determine the number of hours until the battery is only 50% charged.

5. Radioactive iodine-131 was released in the air at the Chernobyl nuclear accident in Russia on April 26, 1986. Its half-life is 8.1 days.

a) Write an equation which represents the percent left of iodine-131 after t days.

b) Determine to the nearest day, how long it took the level of radiation to reduce to 6%.

6. 20% of a certain radioactive isotope decays in 7 days. What is the half-life of the isotope?

7. Radioactive strontium-90 has a half-life of 28 days. A nuclear power plant has 500 kg of strontium to dispose of.

a) How much strontium-90 is remaining after 65 days?

b) How long will it be until only 1 kg is remaining?

8. What is the half-life, to the nearest year, of a radioactive isotope if it takes 8 years for 750 grams to decay to 45 grams?

9. Calculate the number of years for an investment of $2000 to double at an interest rate of 4.5% compounded quarterly.

Answers: 1. a) 10.6 years b) 6.1 years 2. a) [pic] b) 11. 7 years c) [pic] 3. a) 17.0 m b) [pic] 4. a) [pic] b) 4.3 h 5. a) [pic] b) 33 days 6. 21.7 days 7. a) 100 kg b) 251 days 8. 2.0 years 9. 15.5 years

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