a Create three different functions that reflect the amount of miles is earned/spent during the year.
B
b Find the highest number in the table from Part A.
C
c The outgoing balance during one year is the incoming balance of the next year.
D
d What is the net change in miles during last year?
A
a See solution.
B
b 28 900 miles in the end of May.
C
c 5600 miles
D
d No, see solution.
Practice makes perfect
a From the exercise, we know that Tino starts out with 12 000 points. This means at the beginning of the year to the end of January at, his points sits at 12 000.
We have been given information about how much Tino flies earns when he flies his different routes and how much he withdraws. This information, can be written as separate functions with different domains.
ll
Seattle/Kansas City & Function
+3000 points & f(x)=3000
Every month & x={ 1,2,..., 12} [2em]
Seattle/LA & Function
+1900 points & g(x)=1900
Every third month& x={ 3,6,9, 12} [2em]
Withdrawals & Function
-25 000 points & w(x)=-25000
Every 6 months & x={ 6, 12 }
With this information, we can create a table that shows how many frequent flier miles is added/subtracted each month and the cumulative, or total number of frequent flier miles Tino has in his account.
|c|c|c|c|
-4pt x -4pt & -2pt f(x)+g(x)+w(x) -2pt & -4pt Added -4pt & -2pt Total -2pt
-4pt 1 -4pt & -2pt f( 1)+g(1)+w(1) -2pt & -4pt3000 -4pt& -2pt 15 000 -2pt
-4pt 2 -4pt & -2pt f( 2)+g(2)+w(2) -2pt & -4pt3000 -4pt & -2pt 18 000 -2pt
-4pt 3 -4pt & -2pt f( 3)+g( 3)+w(1) -2pt & -4pt4900 -4pt & -2pt 22 900 -2pt
-4pt 4 -4pt & -2pt f( 4)+g(4)+w(4) -2pt & -4pt3000 -4pt& -2pt25 900 -2pt
-4pt 5 -3pt & -2pt f( 5)+g(5)+w(5) -2pt & -4pt3000 -4pt & -2pt 28 900 -2pt
-4pt 6 -3pt & -2pt f( 6)+g( 6)+w( 6) -2pt & -4pt - 20 100 -4pt& -2pt8800 -2pt
-4pt 7 -3pt & -2pt f( 7)+g(7)+w(7) -2pt & -4pt3000 -4pt & -2pt 11 800 -2pt
-4pt 8 -3pt & -2pt f( 8)+g(8)+w(8) -2pt & -4pt3000 -4pt & -2pt 14 800 -2pt
-4pt 9 -3pt & -2pt f( 9)+g( 9)+w(9) -2pt & -4pt4900 -4pt & -2pt19 700 -2pt
-4pt 10 -3pt & -2pt f( 10)+g(10)+w(10) -2pt & -4pt3000 -4pt & -2pt22 700 -2pt
-4pt 11 -3pt & -2pt f( 11)+g(11)+w(11) -2pt & -4pt 3000 -4pt & -2pt25 700 -2pt
-4pt 12 -3pt & -2pt f( 12)+g( 12)+w( 12) -2pt & -4pt - 20 100 -4pt& -2pt 5600 -2pt
Now we can draw the final graph.
b From the table in Part A, we see that Tino had the most amount of miles in May. At this point his miles totaled 28 900
c Because the miles Tino has at the end of December last year will be the same as the amount he has in January this year, we look at December to find his miles at the beginning of the year. That was 5600 points.
d By subtracting the incoming balance from the outgoing balance during the year, we can find the net change.
5600-12 000=- 6400 miles
He spent 6400 more miles than he earned. At the beginning of this year he had 5600 miles in his account. Therefore, If Tino continues this pattern, he would have a negative balance by the end of the year. Therefore, he will not be able to go on both of his usual holidays.
