Name: O . Thursday Applications of Logarithms Assignment - Monday Complete indicated problems on a new sheet of paper each day. 1. Five thousand dollars is invested at 4.5% compounded quarterly will grow to what amount in 25 years? 2. A house bought for $125,000 in 1970 will be worth what amount in 2012 if it appreciates at 3.9% annually? 3. What is the decay constant for a radioactive isotope that decays from 45 gram to 17.3 in 8,400 years? 4. A car depreciates from $15,999 to $8,743 in five years. What is the annual rate of depreciation? 5. What amount would have to be invested in an account that pays 4.75% interest compounded quarterly to grow to $50,000 in 35 years? 6. How long will it take $7,415.25 to double if it is invested at 5.5% compounded monthly? 7. What is the half-life of a radioactive substance with a decay constant of -0.000428? 8. Forty percent of a radioactive isotope remains after 12,000 years. What is the decay constant for this substance? 9. A culture of bacteria grows exponentially. If 325 bacteria grow to 417 in 2 hours, how many will there be after 24 hours? 10. The value of a collectible item went from $1,500 to $2,100 in 2 years. a. What is the rate of appreciation? b. What will the value be in 27 years? c. How long until the $1,500 item is worth $10,000? 11. $15,000 invested at 6.75% for 40 years. What will the investment be worth if it is compounded daily? 12. The model for the number of people at TCHS (n) who have heard a rumor after d days is 71 = 500(1 - e-1:64). How long until 400 people have heard the rumor? 13. Kim invested $2,300 in a corporate bond that pays 14% interest compounded continuously. How long will it take for Kim's investment to be $7000? 14. The 1980 population of the US was approximately 231 million, and the population has been growing continuously at a rate of 1.03% per year. Predict the population of the US in the year 2013 if this trend continues. 15. Suppose that the isotope Californiam-252 has half-life of 2.645 years. What is the decay constant of Californiam-252? 16.If a 325 mg sample of radioactive material decays to 195 mg in 72 hours, find the half-life of the element. 17. If $2500 was invested 6 years ago, and the interest was compounded quarterly, what was the interest rate if the current value is $3425