Step 1 :The problem is asking for the price of a car model in 3.9 years given that the price today is $12,000 and it increases at a constant rate of $820 per year. This is a linear function problem where the independent variable is time (t) in years and the dependent variable is the price (p) in dollars.
Step 2 :The linear function can be represented as \(p = mt + b\) where m is the slope (rate of increase per year) and b is the y-intercept (initial price). In this case, \(m = 820\) and \(b = 12000\).
Step 3 :We need to find the price in 3.9 years, so we substitute \(t = 3.9\) into the equation and solve for p.
Step 4 :Substituting the values into the equation, we get \(p = 820 * 3.9 + 12000\).
Step 5 :Solving the equation, we get \(p = 15198\).
Step 6 :Final Answer: The price of the car in 3.9 years will be \(\boxed{15198}\).