Final answer:
To determine the value of the car in terms of the number of years since 2011, we can use a linear function or an exponential function. The linear function f(t) is given by f(t) = 12,000 - 2,050t, where t is the number of years since 2011. The exponential function g(t) can be found by solving the equations using the values of the car in 2011 and 2013.
Step-by-step explanation:
To determine the value of your car (in dollars) in terms of the number of years t since 2011, we can use a linear function. Let's define the function f(t) as the value of the car in year t. We know that in 2011, the car was worth $12,000, and in 2013, it was worth $7,900. So, the rate of decrease per year is (7,900 - 12,000)/(2013 - 2011) = -2,050. Therefore, the function f(t) can be written as f(t) = 12,000 - 2,050t.
If the value of your car decreased exponentially, we can use an exponential function. Let's define the function g(t) as the value of the car in year t. We know that in 2011, the car was worth $12,000, and in 2013, it was worth $7,900. Using these values, we can write the equation for exponential decay as g(t) = a * e^(k*t), where a is the initial value, e is Euler's number (approximately 2.71828), k is the growth/decay constant, and t is the number of years since 2011.
To find the values of a and k, we can use the given values for 2011 and 2013: 12,000 = a * e^(k*0) and 7,900 = a * e^(k*2). Solving these two equations, we can find the values of a and k to complete the function g(t).