Transcription of Solving Logarithmic Equations (Word Problems)
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Solving Logarithmic Equations (Word Problems)
Solving Logarithmic Equations ( word problems ) Example 1 INVESTMENT Mr. and Mrs. Mitchell are saving for their daughter s college education. They invest $10,000 in an account that pays interest compounded continuously with the goal to have twice that amount in the account in ten years. a. Will the Mitchell s reach their investment goal in ten years? Find the doubling time for the Mr. and Mrs. Mitchell s investment. For continuously compounded interest, the constant k is the interest rate, written as a decimal. t = ln 2k = ln The decimal for is years Use a calculator. Ten years is not enough time for their investment to double. b. What interest rate is required for an investment with continuously compounded interest to double in 10 years? t = ln 2k 10 = ln 2k k = ln 210 solve for k. k years An interest rate of is required for an investment with continuously compounded interest to double in 10 years.
Use LinReg(ax+b) on the STAT CALC screen to find the linear regression equation. We can use the equation ln y = 0.5704x + 3.9699 to model ln y. c. Use the linear regression equation to find an exponential model for the original data. To find a model solve the regression equation in part b for y. ln y = 0.5704x + 3.9699
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