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Victor I think one of the credit card remaining on a phone card (in dollars) in a linear function of the total calling time made the card (in minutes). The remaining credit after 35 minutes of calls is 15.80, and the remaining credit after 63 minutes of calls is 12.44. What is remaining credit after 71 minutes calls?



Answer :

We will determine the credit after 71 minutes as follows:

Now, since it is linear we have that it will be defined by a line [And we are given two different points] so we find the slope:

[tex]m=\frac{12.44-15.80}{63-35}\Rightarrow m=-\frac{3}{25}[/tex]

Now, using one of the points given and the slope we replace in the following expression:

[tex]y-y_1=m(x-x_1)[/tex]

That is:

[tex]y-15.80=(-\frac{3}{25})(x-35)\Rightarrow y-15.80=-\frac{3}{25}x+\frac{21}{5}[/tex][tex]\Rightarrow y=-\frac{3}{25}x+20[/tex]

Now, we replace the time given (71 minutes) and solve:

[tex]y=-\frac{3}{25}(71)+20\Rightarrow y=11.48[/tex]

So, the credit after 71 minutes is $11.48.

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