SOLUTION: 7. Michael is shopping for a new CD player with a built-in alarm clock. Electronics City has a special coupon for $30 off any CD player and is also having a sale with a 25% dis

Question 86219:
7. Michael is shopping for a new CD player with a built-in alarm clock. Electronics City has a special coupon for $30 off any CD player and is also having a sale with a 25% discount on any alarm clock.
a. Write a function rule to model a 25%-off sale, and a function rule to model a $30-off coupon.
b. Use composition of functions to model how much Michael would pay for a CD alarm clock if the clerk applies the discount first and then the coupon.
c. Use composition of functions to model how much Michael would pay for a CD alarm clock if the clerk applies the coupon first and then the discount.
d. Michael selects a CD alarm clock with a regular price of $150. How much more will the item cost if the clerk applies the coupon first?
e. Why does the CD alarm clock cost less if the discount is applied after the coupon?
8. The radius of a balloon is given by r = 0.3t, where t is the time it takes to blow up the
balloon. The volume of a sphere is given by V=4/3IIr^3
a) Find an equation for the composite function V(r(t)).
b) What is the input and output of the composite function?
c) Find the Volume of a balloon 5 seconds after blowing it up.

Answer by scianci(186) (Show Source): You can put this solution on YOUR website!
7. let x = original price of CD player
a. 25% off: .75x [after deducting 25%, the price is 75% of what it was initially]
$30 off: x - 30
b. .75x - 30
c. .75(x - 30)
d. .75(150 - 30) = .75(120) = $90
e. because by applying the discount first the initial price is lowered by 25%, then $30 is taken off the lower price. Otherwise, you'd be deducting $30 from the full price instead of from the lowered price, then taking 25% off the reduced price, which is less of a deduction than taking 25% of the full original price.
8a. V(r(t)) = pi* = pi* = 0.036pi =
b. input is t [time] and output is V [volume]
c. V = =
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