Disposable income, the amount left after taxes have been paid, is one measure of the health of the economy. Using U.S. Energy Information Administration data for selected years from 2015 and projected to 2040, the U.S. real disposable income per capita (in dollars) can be approximated by the equation I = 707.6t + 39,090 where t is the number of years after 2015. (a) What t-value corresponds to 2021? t = (b) Find the predicted U.S. per capita real disposable income (to the nearest $10) in 2021. $ (c) In what year is the U.S. per capita real disposable income expected to exceed $55,000? Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $6600 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) = (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) = (d) Find C(200). C(200) = A manufacturer sells belts for $13 per unit. The fixed costs are $2500 per month, and the variable cost per unit is $8. (a) Write the equations of the revenue R(x) and cost C(x) functions. R(x) = C(x) = (b) Find the break-even point. It takes units to break even.
Disposable income, the amount left after taxes have been paid, is one measure of the health of the economy. Using U.S. Energy Information Administration data for selected years from 2015 and projected to 2040, the U.S. real disposable income per capita (in dollars) can be approximated by the equation I = 707.6t + 39,090 where t is the number of years after 2015. (a) What t-value corresponds to 2021? t = (b) Find the predicted U.S. per capita real disposable income (to the nearest $10) in 2021. $ (c) In what year is the U.S. per capita real disposable income expected to exceed $55,000? Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $6600 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) = (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) = (d) Find C(200). C(200) = A manufacturer sells belts for $13 per unit. The fixed costs are $2500 per month, and the variable cost per unit is $8. (a) Write the equations of the revenue R(x) and cost C(x) functions. R(x) = C(x) = (b) Find the break-even point. It takes units to break even.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Disposable income, the amount left after taxes have been paid, is one measure of the health of the economy. Using U.S. Energy Information Administration data for selected
years from 2015 and projected to 2040, the U.S. real disposable income per capita (in dollars) can be approximated by the equation
I = 707.6t + 39,090
where t is the number of years after 2015.
(a) What t-value corresponds to 2021?
t =
(b) Find the predicted U.S. per capita real disposable income (to the nearest $10) in 2021.
$
(c) In what year is the U.S. per capita real disposable income expected to exceed $55,000?
Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $6600 per month. Materials and labor for each helmet of
this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.)
(a) For this helmet, write the function for monthly total costs C(x).
C(x) =
(b) Write the function for total revenue R(x).
R(x) =
(c) Write the function for profit P(x).
P(x)
=
(d) Find C(200).
C(200) =
A manufacturer sells belts for $13 per unit. The fixed costs are $2500 per month, and the variable cost per unit is $8.
(a) Write the equations of the revenue R(x) and cost C(x) functions.
R(x)
=
C(x) =
(b) Find the break-even point.
It takes
units to break even.
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