**Exercises on Logarithm Word Problems - Logarithm and Exponential Applications**

Instead of Logarithm problems, we have some Logarithm Word Problems. Do your best, and don't rush - Take your time, you have all the time in the world.

*Solve the following word problems.*

**1. Brad invested $2,400 in a three year CD that pays four percent componded annually. What is the compound interest and amount that will be in the bank after three years?**

2. Amy invested $5,600 in a five year CD that pays eight percent componded quarterly. What is the compound interest and amount that will be in the bank after five years?

3. Paul borrowed $90 from Greg eight months ago. Today, Paul paid Greg back $102.60. What is the simple annual interest rate that Paul paid?

4. Brad has a government bond that will be worth $10,588.13 in seven years. The bond has an interest rate of 6% that is compounded semiannually. What is the present value of the bond?

5. Brandon bought a government savings bond for $1,100. He was told that when the bond can be cashed in 5 years that he would get $1,444.48. If the interest on the bond is compounded annually, what is the interest rate on the bond?

6. The Arctic Bank offers a five CD that pays 3.8% interest compounded continuously. Jane deposited $5,931. How much will Jane's account be worth in five years?

7. The local government projects that the town will grow at a constant rate of nineteen percent per year. At this rate, how many years will it take the town's population to be four times its current size?

8. The local government projects that the town will grow at a constant rate of twelve percent per year. At this rate, how many years will it take the town's population to double?

9. Brad invested $2,300 in a corporate bond that pays 14% interest compounded continuously. How long will it take for Brad's investment to triple?

10. What is the pH of a solution whose concentration of hydrogen ions is 6.5 × 10-8 moles per liter?

11. Paul is a scientist who measured the intensity of an earthquake to be 121,000 times the reference intensity. If Paul needs to report a Richter scale reading to Albert, a newspaper reporter, what number should Paul tell Albert?

12. An earthquake was reported to have a Richter number of 6. How does the intensity of the earthquake approximately compare with the reference intensity?

13. A certain material decays at a rate of 0.92% per year. How much of 260 grams of the material will be left in 11 years?

14. A certain material decays at a rate of 0.54% per year. How much of 120 grams of the material will decay in 11 years?

15. A material decays at the rate of 0.099% per year. How long will the material take so that only 30% of the original material is left?

16. The Bagel Bank pays 5.1% interest compounded quarterly. What is the effective annual percentage rate (APR)?

17. Amy bought a diamond ring for $6,000. If the value of the ring increases at a constant rate of 3.83% per year, how much will the ring be worth in twenty-one years?

18. Greg bought a gold coin for $9,000. If the value of the ring increases at a constant rate of 1.79% per year, how many years will it be for the ring to be worth $17,978.02?

19. A bacteria population doubles every eight minutes. If the population begins with one cell, how long will it take to grow to 512 cells?

20. A bacteria population doubles every eight minutes. If the population begins with one cell, how long will it take to grow to 2,097,152 cells?

21. A translucent plastic paper reduces the intensity of light that passes through it by eight percent. Amy wants to combine a number of these papers to only allow at the most forty percent of light to pass through. How many translucent plastic papers should Amy use?

22. Jill's investment in a bank account will be worth $3,746.42 in six months. The current value of Jill's account is $3,600. If the bank pays a fixed rate that is compounded monthly, how much will the account be worth in two years?

23. Brad spent $1,200 on a credit card this month. The credit card charges 24.77% interest compounded continuously. If Brad does not have to pay any monthly minimums and makes no payments, how long will it take until Brad owes the credit card company $2,400?

24. The half-life of a radioactive substance is one hundred fifty-three days. How many days will it take for seventy percent of the substance to decay?

25. Brad bought $5,141 worth of office equipment. The government allows for office equipment to be depreciated at an annual rate of 5.5% per year. How long will it take for Brad to depreciate the equipment fifty-four percent?

26. Albert currently pays a $608 premium for health insurance. If the premium increases at an annual rate of 8.01% per year, how many years will it take for the premium to be $2,086.06?

27. Brad created a chart that shows the population of a town will increase to 96,627 people from a current population of 11,211 people. The rate of increase is an annual increase of 4.18%. Brad forgot to include on the graph the number of years this increase will take. How many years should Brad add to the chart?

28. The number of bacteria in a culture grows from 39 to 176 in 1 hour and 19 minutes. How many bacteria will be present in 9 hours and 16 minutes?

-------------------------------------------------------------------