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## how to construct a mathematical model for each plan?

a. A flat fee of \$50 per month for unlimited calls (is it 50=x)

b. a \$30 per month fee for a total of 30 hours of calls and an additional charge of \$0.01 per minute for all calls over 30 hours

c. a \$5 per month fee and a charge of \$0.04 per minute for all calls ( is it 5+.04x)

d. a \$2 per month fee and a charge of \$0.045 per minute for all calls; the fee is waived if the charge for calls is \$20 or more

e. A charge of \$0.05 per minute for all calls; there is no additional fees ( is it .05x)

Let y = the monthly phone cost (bill) and x = the number of minutes for all calls

a.  y = \$50  (y is the cost per month, x is the minutes called, so it's y = 50, not x = 50)

b.  The number of minutes over 30 hours (30 hours*60 minutes per hour = 1800 minutes) is = x-1800

|  \$30 if x ≤ 1800 minutes
y = <
|  \$30 + (\$.01)(x-1800) if x > 1800 minutes

c.   y = \$5 + (\$0.04)x   (Yes, you got this one right!)

|  \$2 + (\$0.45)x  if  (\$0.45)x < \$20
d.  y = <
|  (\$0.45)x  if (\$0.45)x ≥ 20

e.  y = (\$0.05)x   (Yes, you got this one right as well!)