Answer:
a. t = 2.48 will be a period within 2009.
b. 56.16 million
Step-by-step explanation:
Here is the complete question
Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the early years but began to grow rapidly after 2005. But the iPod era is coming to a close. Smartphones with music and video
Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the
END OF THE IPOD ERA
players are replacing the iPod, along with the category of device it helped to create. Sales of the iPod worldwide from 2007
through 2011 (in millions) were
approximately
N(0= -2.65t2 + 13.13t+ 39.9 (0 < t< 4)
in year t, where t= 0 corresponds to 2007. Show that the worldwide sales of the iPod peaked sometime in 2009. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?
a. Show that the worldwide sales of the iPod peaked sometime in 2009
N(t) = -2.65t² + 13.13t + 39.9
To find the maximum value of N(t), we find dN(t)/dt and equate it to zero
dN(t)/dt = d[-2.65t² + 13.13t + 39.9]/dt
dN(t)/dt = -5.3t + 13.13 = 0
-5.3t = - 13.13
t = -13.13/(-5.3)
t = 2.477
t ≅ 2.48
d²N(t)/dt² =d[-5.3t + 13.13]/dt = -5.3 < 0. So, t = 2.48 is a maximum point
Since t = 2 is 2009 and t = 3 is 2010, t = 2.48 will be a period within 2009.
b. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?
The approximate largest number of ipods sold is when t = 2.48
N(2.48) = -2.65(2.48)² + 13.13(2.48) + 39.9
N(2.48) = -16.29856 + 32.5624 + 39.9
N(2.48) = 56.16384
N(2.48) ≅ 56.16 million
