Assignment:
Q1. Solve the equation.
3(6 - 3x) = 1/27
Q2. Use natural logarithms to evaluate the logarithm to the nearest hundredth.
log√4 ^259.5
Q3. Solve the problem.
Sonja and Chris both accept new jobs on March 1, 2001. Sonja starts at $45000
with a raise each March 1 of 3 % Chris starts at $33000 with a raise on March 1 of each year of 8%. In what year will Chris' salary exceed Sonja's?
Q4. Solve the problem.
The sales of a new model of notebook computer are approximated by : S(x) = 5000-13000e^-x/9, where x represents the number of months the computer has been on the market and S represents sales in thousands of dollars. In how many months will the sales reach $2,600,000?
Q5. Solve the problem.
The number of acres in a landfill decreases according to the function B=6300e^-0.05t , where t is measured in years. How many acres will the landfill have after 10 years?
Q6. If inflation is 6% a year compounded annually, what will it cost in 18 years to buy a house currently valued at $116,000?
Q7. A municipal bond with a face value of $10,000 in ten years can be purchased now for $5238. Find the simple interest rate. Round to the nearest tenth of a percent.
Q8. The State Employees' Credit Union offers a 1-year certificate of deposit with an APR (or effective rate) of 5.5%. If interest is compounded quarterly, find the actual interest rate. Round to the nearest tenth of a percent.
Q9. Solve the problem. Round to the nearest cent.
If Bob deposits $5,000 at the end of each year for 13 years in an account paying 5% interest compounded annually, find the amount he will have on deposit.
Q10. Solve the problem. Round to the nearest cent.
Larry wants to start an IRA that will have $950,000 in it when he retires in 19 years. How much should he invest semiannually in his IRA to do this if the interest is 13% compounded semiannually?
Q11. Solve the problem.
Tasha borrowed $15,000 to purchase a new car at an annual interest rate of 11%. She is to pay it back in equal monthly payments over a 4 year period. How much total interest will be paid over the period of the loan? Round to the nearest dollar.
Q12. Find the periodic payment that will render the sum.
S = $590,000, interest is 10% compounded semiannually, payments made at the end of each semiannual period for 8 years.
Provide complete and step by step solution for the question and show calculations and use formulas.