In one area of the country, inflation is causing prices to rise at a rate of $1.4 \%$ per year. If a product costs $\$ 3.62$ in the year 2000 , write an equation that represents the price, $P$, of that product $x$ years after 2000. An equation that represents the price of that product $x$ years after 2000 is $P=$

Step 1 ：The problem is asking for an equation that represents the price of a product x years after 2000, given that the price is increasing at a rate of 1.4% per year. This is a compound interest problem, where the initial amount is the price in 2000, the interest rate is 1.4%, and the number of years is x.

Step 2 ：The general formula for compound interest is: \(P = P0 * (1 + r)^n\) where: \(P\) is the future value of the investment/loan, including interest, \(P0\) is the principal investment amount (the initial deposit or loan amount), \(r\) is the annual interest rate (in decimal), \(n\) is the number of years the money is invested or borrowed for.

Step 3 ：In this case, \(P0\) is $3.62, \(r\) is 1.4% or 0.014, and \(n\) is x. Substituting these values into the formula gives: \(P = 3.62 * (1 + 0.014)^x\)

Step 4 ：This is the equation that represents the price of the product x years after 2000.

Step 5 ：Final Answer: \(\boxed{P = 3.62 \times (1 + 0.014)^x}\)