Derivative as a rate of change.pptx - The Derivative as a Rate of Change 1 Example 1 It is estimated that x months form now the population of a certain

Derivative as a rate of change.pptx - The Derivative as a...

  • No School
  • AA 1
  • 18

This preview shows page 1 - 6 out of 18 pages.

1 The Derivative as a Rate of Change
Image of page 1

Subscribe to view the full document.

2 It is estimated that x months form now, the population of a certain community will be Example 1 8000 20 ) ( 2 x x x p a. At what rate will the population be changing with respect to time 15 months from now? b. By how much will the population actually change during the 16 th month?
Image of page 2
3 Solution: a. The rate of change of the population with respect to time is the derivative of the population function. That is 20 2 ) ( change of Rate x x p The rate of change of the population 15 months from now will be month per people 50 20 ) 15 ( 2 ) 15 ( p b. The actual change in the population during the 16 th month is people 51 8525 8576 ) 15 ( ) 16 ( p p Note : Since the rate varies during the month, the actual change in population during 16 th month differs from the monthly rate of the change at the beginning of the month.
Image of page 3

Subscribe to view the full document.

4 Relative and Percentage Rates of Change : The relative rate of change of a quantity Q(x) with respect to x is given by the ratio The corresponding percentage rate of change of Q(x) with respect to x is Q dx dQ x Q x Q Q(x) / ) ( ) ( of change of rate Relative ) ( ) ( 100 ) ( of change of rate Percentage x Q x Q x Q Relative and Percentage Rates of Change
Image of page 4
5 Example 2 The gross domestic product (GDP) of a certain country was billion dollars t years after 1995. a. At what rate was the GDP changing with respect to time in 2005? b. At what percentage rate was the GDP changing with respect to time in 2005? 106 5 ) ( 2 t t t N Solution: a. The rate of change of the GDP is the derivative N’(t)=2t+5.
Image of page 5

Subscribe to view the full document.

Image of page 6

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes