PP 7.5 - Exponential Growth and Decay Exponential Model If...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Exponential Growth and Decay
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Exponential Model If y(t) is the value of a quantity at time t and if the rate of change of y with respect to t is proportional to its size y(t) at any time, then ky dt dy = k is a constant, called the constant of proportionality.
Image of page 2
Comments If k is positive, then the model represents natural or exponential growth. If k is negative, then the model represents natural or exponential decay. ky dt dy = This is a differential equation because it involves y and its derivative.
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Theorem kt e y t y ) 0 ( ) ( = The only solutions of the exponential model are the exponential functions kt e y t y ky dt dy ) 0 ( ) ( : s other word In = =
Image of page 4
Example 1. Determine an differential equation for Q(t). Exponential model: kQ dt dQ = The rate at which a radioactive substance decays is proportional to the amount Q(t) of the substance remaining at time t. 2. Find the solution of the equation, assuming that initially there were 15 kg of the substance and that its half-life is 120 years.
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Solution kt e Q t Q kQ dt dQ ) 0 ( ) ( = = 5 . 7 ) 120 ( and 15 ) ( = = Q
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

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