Math  /  Algebra

QuestionDerive a rule for estimating the "years to triple"-that is, the number of years it would take for the general levels of prices to triple for a given annual inflation rate.
Let the annual inflation rate be the numerical part of the rate written as a percentage. Select the correct choice below and fill in the answer box to complete your choice. (Round to the nearest whole number as needed.) A. years to triple =10ln3 annual inflation rate  annual inflation rate =\frac{10 \ln 3}{\text { annual inflation rate }} \approx \frac{\square}{\text { annual inflation rate }} B. years to triple =100ln3 annual inflation rate  annual inflation rate =\frac{100 \ln 3}{\text { annual inflation rate }} \approx \frac{\square}{\text { annual inflation rate }} C. years to triple =ln3 annual inflation rate  annual inflation rate =\frac{\ln 3}{\text { annual inflation rate }} \approx \frac{\square}{\text { annual inflation rate }} D. years to triple = annual inflation rate ln3 annual inflation rate =\frac{\text { annual inflation rate }}{\ln 3} \approx \frac{\text { annual inflation rate }}{\square} E. years to triple = annual inflation rate 100ln3 annual inflation rate =\frac{\text { annual inflation rate }}{100 \ln 3} \approx \frac{\text { annual inflation rate }}{\square} F. years to triple = annual inflation rate 10ln3 annual inflation rate =\frac{\text { annual inflation rate }}{10 \ln 3} \approx \frac{\text { annual inflation rate }}{\square}

Studdy Solution
Compare with the given choices. The derived formula is:
t=ln3r t = \frac{\ln 3}{r}
This matches choice C. To find the approximate numerical value, calculate ln31.0986 \ln 3 \approx 1.0986 , so:
t1.0986r t \approx \frac{1.0986}{r}
Rounding 1.0986 1.0986 to the nearest whole number gives approximately 1, so:
t1r t \approx \frac{1}{r}
However, choice C is the closest match without rounding:
tln3r t \approx \frac{\ln 3}{r}

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