I just completed Trigonometry and College Algebra, and i'm heading into Calculus, so i thought i would get a head start on the material. So right now i'm working out of an old calculus book i got at the library. Then i came across this problem:(adsbygoogle = window.adsbygoogle || []).push({});

A dial-direct long distance call between two cities costs $1.04 for the first 2 minutes and $0.36 for each additional minute or fraction thereof.

a.) Use the greatest integer function to write the cost C of a call in terms of the time t (in minutes). Graph the cost function and discuss its continuity.

b.) Find the cost of a 9-minute call.

I didn't think this would be so hard, so i worked at it a little bit, the only part i had trouble with was coming up with the correct function, graphing and solving for 9 minutes is easy after that. I got:

C(t) = 1.04, 0 < t <= 2

1.04 + 0.36 * greatest integer of (t - 2 ), t > 2

So i doulble checked in the back of the book and it says the answer is:

C(t) = 1.04, 0 < t <= 2

1.04 + 0.36 * greatest integer of (t - 1), t > 2, t is not an integer

1.04 + 0.36(t - 2), t > 2, t is an integer

i don't understand why there needs to be to seperate functions for it being an integer or not. I thought with greatest integer, if the number is already an integer, it would leave it alone, and also, why only t - 1 in the second one, shouldn't it be t - 2?

Anyways, i hope someone will help me out. Thanks!

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# Homework Help: Greatest Integer Problem

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