1 / 5

Composite Functions: Application

Example: The monthly demand, D , for a product, is. where p is the price per unit of the product. The price per unit, p , for the product is p = 2000 – 10 t , where t is the number of months past January 1995. Write the monthly demand, D , as a function of t. D p.

hila
Download Presentation

Composite Functions: Application

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Example: The monthly demand, D, for a product, is where p is the price per unit of the product. The price per unit, p, for the product is p = 2000 – 10t, where t is the number of months past January 1995. Write the monthly demand, D, as a function of t. D p Note, D is a function of p, D(p) and p is a function of t. p(t) t (D p)(t) = Composite Functions: Application Compute (D p)(t) = D(p(t)).

  2. (D p)(t) = This is now a function of demand with respect to t, so can be relabeled, D(t) = 6250 = Composite Functions: Application When will the monthly demand reach 6,250 units? 6250(2000 – 10t) = 5000000, 12500000 – 62500t = 5000000, - 62500t = - 7500000, t = 120 months The monthly demand will reach 6,250 units in January 2005. Slide 2

  3. Try: An observer on the ground is 300 feet away from the launching point of a balloon. The balloon is rising is 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). Jot down the figures above and click to see the questions! d x 300 feet Composite Functions: Application Slide 3

  4. d x 300 feet Composite Functions: Application (a) Express d as a function of x. Hint: Use the Pythagorean Theorem. (b) Express x as a function of t. x(t) = 10t (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. It takes 40 seconds. Slide 4

  5. Composite Functions: Application END OF PRESENTATION Click to rerun the slideshow.

More Related