A phone company has a texting plan that charges a monthly rate based on the number of texts an individual sends per month. This is modeled by the function cost of plan, 𝐶(𝑥),𝐶(𝑥), in dollars, is a function of the number of texts sent, 𝑥𝑥, per month.𝐶(𝑥)=⎧⎩⎨⎪⎪250.05𝑥+25.075𝑥+25 if 𝑥<100 if 100≤𝑥≤500 if 500<𝑥𝐶(𝑥)={25 if 𝑥<1000.05𝑥+25 if 100≤𝑥≤500.075𝑥+25 if 500<𝑥If you sent 500500 texts last month, what was the cost of your bill from the phone company? Question 2Answera.$37.50$37.50 b.$50.00$50.00c.$25.00$25.00d.$62.50
Question
A phone company has a texting plan that charges a monthly rate based on the number of texts an individual sends per month. This is modeled by the function cost of plan, 𝐶(𝑥),𝐶(𝑥), in dollars, is a function of the number of texts sent, 𝑥𝑥, per month.𝐶(𝑥)=⎧⎩⎨⎪⎪250.05𝑥+25.075𝑥+25 if 𝑥<100 if 100≤𝑥≤500 if 500<𝑥𝐶(𝑥)={25 if 𝑥<1000.05𝑥+25 if 100≤𝑥≤500.075𝑥+25 if 500<𝑥If you sent 500500 texts last month, what was the cost of your bill from the phone company? Question 2Answera.37.50 b.50.00c.25.00d.$62.50
Solution
The cost of the plan is determined by the number of texts sent. According to the function given, if the number of texts (x) is between 100 and 500, the cost (C(x)) is calculated as 0.05x + 25.
Given that you sent 500 texts last month, we substitute x with 500 in the equation:
C(500) = 0.05*500 + 25 = 25 + 25 = $50.00
So, the cost of your bill from the phone company last month was 50.00.
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