Suppose you own a car that is 40 months old. From an automobile dealer's "Blue Book" you find that its trade-in value is $3200. From an old Blue Book you find
that its trade-in value 10 months ago was $4700.
a. Write a function expressing trade-in value as a function of the cars age in
months.
b. You plan to get rid of the car when its trade-in value drops to $1000. How
much longer should you keep the car?
c. What does the slope of your function represent in the real world? Why is
it negative?
d. When do you predict that car will be worthless? How do you know this?
e. According to your model, what was the trade-in value of the car when it
was new?

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12