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Composite Functions: Application PowerPoint Presentation

Composite Functions: Application

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Composite Functions: Application

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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)).

(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

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).

Jot down the figures above and click to see the questions!

d

x

300 feet

Composite Functions: Application

Slide 3

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) todetermine how long it takes from launching for the balloonto be 500 feet from theobserver.

It takes 40 seconds.

Slide 4

Composite Functions: Application

END OF PRESENTATION

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