Question

what is the doubling time of prices which are increasing by 2 percent per year? doubling time = (include units)

Explanation:

Step1: Use rule of 70 approximation

The rule of 70 estimates doubling time as $\frac{70}{\text{growth rate (percent)}}$.

Step2: Plug in 2% growth rate

$\text{Doubling time} = \frac{70}{2}$

Step1: Set up doubling equation

$2P_0 = P_0(1+0.02)^t$

Step2: Cancel $P_0$, take natural log

$\ln(2) = t\ln(1.02)$

Step3: Solve for t

$t = \frac{\ln(2)}{\ln(1.02)}$

Step4: Calculate value

$t \approx \frac{0.6931}{0.0198} \approx 35$

Answer:

35 years

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For a precise calculation using the exponential growth formula $P(t) = P_0(1+r)^t$ where $P(t)=2P_0$ and $r=0.02$: