Question 2
$2 \mathrm{pts}$
Select the equation that will best mochel the situation below.
Situation: The price of a Big Mac is often used to provide a true estimate of inflation and to compare purchasing power around the world. (Government estimates of inflation are sometimes questionable.) In 2020 a Big Mac cost about \$3.69 in Ohio. In 2023 the average Ohio price is about $\$ 5.17$. Using the function $P(t)=P_{0} e^{r t}$, compute an estimate of the annual inflation rate from 2020 to 2023. (Report your answer to three decimals of accuracy.)
The estimated annual percent of inflation is about

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 \(\boxed{11.242\%}\).