Functions that Describe Situations

Key Questions

  • Why do you write functions to describe real life situations?

    Suppose we were asked to find the volume of a balloon

    we will use the function of volume for a balloon

    #v(ballon)=#4/3 pi r^3##

    we know radius is 3

    #4/3 *pi 3^3#

    #4 pi* 9#

    #36pi#

    Hence there several functions which are much more complex than this.

    Sidharth · 1 · Jan 5 2015
  • What is an example of a function that describes a situation?

    Consider a taxi and the fare you have to pay to go from A street to B avenue and call it #f#.

    #f# will depend upon various things but to make our life easier let assume that depends only upon the distance #d# (in km).
    So yo can write that "fare depends upon distance" or in mathlanguage: #f(d)#.

    A strange thing is that when you sit in the taxy the meter already shows a certain amount to pay...this is à fixed amount you have to pay no matter the distance, let's say, #2$#.
    Now for each km travelled the taxi driver has to pay petrol, maintenance of the vehicle, taxes and get money for himself...so he will charge #1.5$# for each km.
    The meter of the taxi will now use the following function to evaluate the fare:
    #f(d)=1.5d+2#
    This is called "linear" function and allows you to "predict" your fare for each distance travelled (even if #d=0#, i.e., when you only sit in the taxi!)
    Now, let us assume that the distance #d# between A street and B avenue is #d=10 km#, you fare wiĺ be:
    #f(10)=1.5×10+2=17$#

    You can now improve your function including additional costs and dependences or build new relationships.

    Gió · 1 · Jan 19 2015

Questions

Expressions, Equations, and Functions