Practice Exam in Mathematics: Solving Equations, Logarithms, and Interest Problems - Prof., Exams of Mathematical Methods for Numerical Analysis and Optimization

Download Practice Exam in Mathematics: Solving Equations, Logarithms, and Interest Problems - Prof. and more Exams Mathematical Methods for Numerical Analysis and Optimization in PDF only on Docsity! Practice Exam 2 1. Solve the following equations for x. i. 16x+3 = 642x−5 ii. log2(5x− 2)− log2(x + 3) = 2 iii. ln(x + 2) = 2 2. Use the properties of logs to combine each of the following into one log. i. (3x− 4) ln y + ln (x + 2)− ln (x3 − x + 2) ii. 3 log4 r 2 − 2 log4 r 3. The quantity (in grams) of a radioactive substance present at time t is Q(t) = 1000 ( 5−0.3t ) i. How much will be present in 6 months? ii. How long will it take to reduce the substance to 8g? 4. If your bank charges 5.6% interest compounded monthly, what is the effective interest rate? What if the interest is compounded daily? 5. Find the present value of an ordinary annuity with quarterly payments of $4,000 at 5% (compounded quarterly) for 10 years. 6. Vincent Vega decides to by a $750,000 house. He puts 50% down and finances the rest by taking out a 20-year mortgage at 4% (compounded monthly). What are his monthly payments? 1