Assignment 65
1. Using the laws of logarithms, write each expression as a single logarithm:
2. Evaluate each expression. You should be able to do each one without a calculator.
3. State the domain and range for the function y = log_{7}(x-12)? 4. Solve each equation. (Remember, you should check for extraneous solutions since log is a restricted function.)
5. Growth and Decay problems:
6. If f(x) = y = 5 + log_{12}(x+5), then f^{-1}(x) = 7. The table gives the mean weight w (in kilograms) and age x (in years) of Atlantic cod from the Gulf of Maine. Check to see if an exponential model is a good fit for the data.
Problem: Solve for x: log_{7}(x+8) = log_{7}(x) + 2. Solution (with communication): log_{7}(x+8) = log_{7}(x) + 2 ==> log_{7}(x+8) - log_{7}(x) = 2 ==> log_{7}[(x+8)/x] = 2 ==> (x+8)/x = 7^{2 }= 49 ==> x + 8 = 49x ==> 48x = 8 ==> x = 1/6. Problem: How long will it take a single deposit to increase 20-fold if the annual interest rate is 18%? Solution (with communication): If T is the requested number of years, then (1.18)^{T} = 20 ==> T = log_{1.18}20 = log(20)/log(1.18) ==> T = 18.0995. Rounding up, it would take 19 years for $1 to grow to $20 if the annual interest rate is 18%. |