A cell phone plan has a basic charge of \ 35amonth.Theplanincludes400freeminutesandcharges10centsforeachadditionalminuteofusage.WritethemonthlycostCasafunctionofthenumberxofminutesusedandgraphCasafunctionofxfor0\leqslant x \leqslant 600 .$

Question

Filo · Accepted Answer

Key Concepts: Cell Phone Plan, Monthly Cost, Free Minutes, Additional Minute Charge, Function, Graph

Explanation:
The monthly cost of the cell phone plan depends on the number of minutes used. For the first 400 minutes, the cost is \35.Foreachadditionalminute,thecostis10cents.Thismeansthatthemonthlycostisalinearfunctionofthenumberofminutes,withaslopeof0.1anday−interceptof35.StepbyStepSolution:Step1.TowritethemonthlycostC as a function of the number of minutes x, we can use the formula:

Step 2. C(x)=35+0.1(x−400), where x>400, as the cost is \35 for the first 400 minutes

Step 3. For x⩽400, the cost is \35,soC(x) = 35.$

Step 4. To graph the function C(x), we can plot the y-intercept of (0,35) and use the slope of 0.1 to find additional points on the line. We can then connect the dots to get a straight line. The domain of C(x) is [0,600].

Final Answer:
The monthly cost C as a function of the number of minutes x is: 
C(x)={35,35+0.1(x−400),​0⩽x⩽400x>400​

The graph of this function is a straight line with a y-intercept of (0,35) and a slope of 0.1 over the domain [0,600].

Question Text	A cell phone plan has a basic charge of \ 35 $am o n t h . T h e pl anin c l u d es 400 f ree min u t es an d c ha r g es 10 ce n t s f ore a c ha dd i t i o na l min u t eo f u s a g e . W r i t e t h e m o n t h l ycos t$ C $a s a f u n c t i o n o f t h e n u mb er$ x $o f min u t es u se d an d g r a p h$ C $a s a f u n c t i o n o f$ x $f or 0$ \leqslant x \leqslant 600 .$
Topic	All Topics
Subject	AP Calculus BC
Class	Class 11
Answer Type	Text solution:1

Text solutionVerified

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