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Algebra II Homework Week 13 Monday (11/26) – 1 𝑥 1. Graph 𝑦 = 3 (2) . Then state the domain and range. 2. Determine whether each function represents exponential growth or decay. 1 𝑥 b. 𝑦 = .4(7)𝑥 a. 𝑦 = 2 (6) c. 𝑦 = 3.4(0.1)𝑥 3. Solve the equation 3𝑛−2 = 27 1 𝑦−3 4. Solve (7) = 343 5. Solve 325𝑝+2 ≥ 16 6. Solve 49𝑥 = 7𝑥 2 −15 Tuesday (11/27) – 1. Write each equation in logarithmic form a. 83 = 512 b. 5−3 = 1 1 125 c.1002 = 10 2. Write each equation in exponential form. a. log 5 125 = 3 b. log13 169 = 2 2 c. log 8 4 = 3 3. Evaluate each expression. a. log 2 16 1 c. log 5 57 b. log 2 32 4. Solve each equation or inequality. a. log 9 𝑥 = 2 1 b. log 64 𝑦 ≤ 2 c. log 6 (2𝑥 − 3) = log 6 (𝑥 + 2) Wednesday (11/28) – 1. Use a calculator to evaluate each expression to four decimal places. a. a. log 19 b. log 0.75 2. EARTHQUAKES In 1906, San Francisco experienced a major earthquake of magnitude 8.3. In 1989, another major quake hit the area with a magnitude of 7.1. The amount of energy E, in ergs, an earthquake releases is related to its Richter scale magnitude M by the equation log E = 11.8 + 1.5M. How much more energy did the 1906 quake release than the 1989 quake? 3. Solve 2a + 3 = 34. 4. Solve 5b – 1 ≥ 106 – b. Algebra II Homework Week 13 5. Express log7 58 in terms of common logarithms. Then approximate its value to four decimal places. Thursday (11/29) – 1. Use a calculator to evaluate each expression to four decimal places. a. e2.5 b. e–4.6 2. Use a calculator to evaluate each expression to four decimal places. a. ln 15 b. ln 0.75 3. Write an equivalent exponential or logarithmic equation. a. e–x = 2 b. ln e2a – 5 4. Solve –2e5x + 10 = 6. 5. Solve 6e–x < 15. 6. Solve each equation or inequality. a. ln (6x – 3) + 3 = 10 b. ln (3x + 2) < 5 Friday (11/30) – 1. RECREATION A particular chemical must be added to a swimming pool at regular intervals because it is released from the water into the air at the rate of 5% per hour. Sixteen ounces of the chemical is added at 8 am. At what time will three–fourths of this chemical be gone from the pool? 2. Exponential Decay of the Form y = ae–kt. CHEMISTRY The half–life of a radioactive substance is the time it takes for half of the atoms of the substance to decay. Each element has a unique half–life. Radon–222 has a half–life of about 3.8 days, while thorium–234 has a half–life of about 24 days. Find the value of k for each element and compare their equations for decay. 3. In 1980, the value of farming land in a region of Wyoming was $150 per acre. Since then, the value has increased by exactly 0.75% per year. If the land continues to increase in value at this rate, what will the approximate value of the land per acre be in 2005? A. $610 B. $330 C. $181 D. $175 E. $1098 kt 4. Exponential Growth of the Form y = ae . SAVINGS Sue invests $1000 at 5% interest compounded continuously and Norma invests $1250 at 3.5% interest compounded continuously. When interest is compounded continuously, the amount A in an account after t years is found using the formula A = Pert, where P is the amount of principal and r is the annual interest rate. In how many years will Sue’s account be greater than Norma’s account?