{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Hwang exponential - Holy Cross College Fall Semester 2003...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Holy Cross College, Fall Semester, 2003 Math 131, Professor Hwang Descriptions of Exponential Growth The text has three ways of describing exponential growth. While these three methods are mathematically equivalent, the book’s terminology about “rate of growth/decay” can be confusing, and demands careful attention to wording. General Base Let a > 0 be a positive constant. The general exponential function with base a is a function of the form f ( t ) = P 0 a t . Usually the variable t represents time, measured in units appropriate to a given problem. The constant P 0 represents the amount of “stuff” at time 0. For each increment of t by one unit, an exponential function’s value gets multiplied by a , because f ( t + 1) = P 0 a t +1 = P 0 a t · a = a · f ( t ) . Consequently, if 0 < a < 1, then f is decreasing (by a factor of a for each time unit), while if a > 1, then f is increasing (by a factor of a for each time step). Growth Rate When a population grows at a rate of 2 . 6% per year, the number of individuals
Image of page 1
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