Problema Solution
Suppose that in the year 2000, the cost of a compact car averaged $ 12700 and that in 2003, the cost averaged $ 15100. Assuming that the relationship between year t and cost c is linear, develop a formula for predicting the average cost of a compact car in the future measuring the variable t as years since 2000.
my formula is Q=Q_(1+r)^ Q_ = 12,700 R = needed Q= 15,100 T= 3 ? I am lost after this
What do you predict the average cost of a compact car will be in the year 2007? .
Answer provided by our tutors
Let t be the number of years since 2000 and c be the cost of the car.
The two points we have are (0, 12,700) and (3, 15,100).
We can use the point-slope form of a line to write a linear equation: y-y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points. In this case, we will use t for x and c for y. First, we have to find the slope.
m = (c2-c1)/(t2-t1) = (15,100 - 12,700)/(3-0) = 2400/3 = 800.
Substituting that into the above formula, we have c - 12700 = 800(t-0).
Solve for c by distributing the 800: c - 12700 = 800t
and then add 12700 to each side: c = 800t + 12700
To predict the cost of a car in 2007, which is 7 years since 2000, plug in 7 for t:
c = 800(7) + 12700
c = 5600 + 12700
c = 18300
So, the predicted cost of the compact car in 2007 is $18,300.