Use logarithms to solve the problem. The rule of 70 is a rule of thumb for estimating the doubling time of a quantity (e.g., investment, GDP, population) experiencing growth that is compounded continuously. The rule states that if the growth rate is r% per year, then the time it takes for the quantity to double is approximately 70/r years. (a) Use the rule of 70 to estimate the time it takes for an investment to double in value if it grows at the rate of 5% per year compounded continuously. (b) What is the exact time it will take for the investment in part (a) to double in value? (Round your answer to two decimal places.)
Use logarithms to solve the problem. The rule of 70 is a rule of thumb for estimating the doubling time of a quantity (e.g., investment, GDP, population) experiencing growth that is compounded continuously. The rule states that if the growth rate is r% per year, then the time it takes for the quantity to double is approximately 70/r years. (a) Use the rule of 70 to estimate the time it takes for an investment to double in value if it grows at the rate of 5% per year compounded continuously. (b) What is the exact time it will take for the investment in part (a) to double in value? (Round your answer to two decimal places.)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.CT: Chapter Test
Problem 11CT
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Use logarithms to solve the problem.
The rule of 70 is a rule of thumb for estimating the doubling time of a quantity (e.g., investment, GDP, population) experiencing growth that is compounded continuously. The rule states that if the growth rate is r% per year, then the time it takes for the quantity to double is approximately 70/r years.
(a)
Use the rule of 70 to estimate the time it takes for an investment to double in value if it grows at the rate of 5% per year compounded continuously.
(b)
What is the exact time it will take for the investment in part (a) to double in value? (Round your answer to two decimal places.)
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