Step 1 :We are given the initial price of a Big Mac in 2020, \(P_0 = 3.69\), and the price in 2023, \(P(3) = 5.17\). We can use the formula for exponential growth, \(P(t) = P_0 e^{rt}\), to solve for the rate of inflation, \(r\).
Step 2 :We can rearrange the formula to solve for \(r\): \(r = \frac{1}{t} \ln \left( \frac{P(t)}{P_0} \right)\)
Step 3 :Substitute the given values into the formula: \(P_0 = 3.69\), \(P_t = 5.17\), and \(t = 3\).
Step 4 :Calculate the result to get \(r = 0.1124154101559673\). This is the annual inflation rate in decimal form.
Step 5 :To convert it to a percentage, we multiply by 100 to get \(r_{\text{percent}} = 11.24154101559673\).
Step 6 :Final Answer: The estimated annual percent of inflation is about \(\boxed{11.242\%}\).