Table of Contents Composite Functions: Application The price per unit, p, for the product is p = 2000 – 10t, where t is the number of months past January Example: The monthly demand, D, for a product, is where p is the price per unit of the product. Write the monthly demand, D, as a function of t. Compute (D  p)(t) = D(p(t)). Note, D is a function of p, D(p)D(p) DpDp (D  p)(t) = and p is a function of t. t p(t)p(t)

Table of Contents Composite Functions: Application Slide 2 (D  p)(t) = When will the monthly demand reach 6,250 units? This is now a function of demand with respect to t, so can be relabeled,D(t) = 6250 = 6250(2000 – 10t) = , – 62500t = , t = , t = 120 monthsThe monthly demand will reach 6,250 units in January 2005.

Table of Contents Composite Functions: Application Slide 3 Try:An observer on the ground is 300 feet away from the launching point of a balloon. The balloon is risingis rising at a rate of 10 feet per second. Let d = the distance (in feet) between the balloon and the observer. Let t = the time elapsed (in seconds) since the balloon was launched. Let x = the balloon's altitude (in feet). 300 feet x d Jot down the figures above and click to see the questions!

Table of Contents Composite Functions: Application (a)Express d as a function of x. Hint: Use the Pythagorean Theorem. Slide feet x d (b)Express x as a function of t. (c)Express d as a function of t. (d)Use the result found in (c) to determine how long it takes from launching for the balloon to be 500 feet from the observer. x(t) = 10t It takes 40 seconds.

Table of Contents Composite Functions: Application