Assignment 62
Example 1:
Example 2:
Problem: Solve for x: 8^{4x} = 64^{x-9}. Solution (with communication): 8^{4x} = 64^{x+9} ==> 8^{4x} = (8^{2})^{x+9} ==> 8^{4x} = 8^{2x+18} ==> 4x = 2x+18 ==> 2x=18 ==>x = 9. Problem: Solve for z: 7^{2z} - 34 = 693. Solution (with communication): 7^{2z} - 34 = 693 ==> 7^{2z }= 693 + 34 = 727 ==> 2z = log_{7}727 = log(727)/log(7) ==> z = (1/2)log(727)/log(7) = 1.693. Problem: Solve for w: ln w - ln 12 = 4. Solution (with communication): ln w - ln 12 = 4 ==> ln(w/12) = 4 ==> w/12 = e^{4 } ==>w = 12e^{4} = 655.178. Problem: A substance decays at a rate of 2.3% a year. How many years will pass before only 25% of the original amount remains? Solution (with communication): If x is the requested number of years, then (1-0.023)^{x} = 0.25 ==>(0.977)^{x} = 0.25 ==> x = log(0.25)/log(0.977) = 59.578. It will take approximately 60 years to lose 75% of the original amount. |