d Substitute t(n)=500 in the equation from Part C.
A
aTable:
Month012345Stamps120132144156168180
B
b264
C
ct(n)=12n+120
D
dn≈31.67,
After 32 months it's filled but with stamps remaining. See solution.
Practice makes perfect
a We know that the stamp club sends Lona 12 new stamps each month. This means the rate of change describing Lona's stamps is constant. Using a table, we can find the number of stamps she receives in months 2,3,4, and 5.
Now we can complete the table.
Month012345Stamps120132144156168180
b Each month she will receive 12 stamps, and there are 12 months in a year. With this information, we can calculate the number of stamps she will receive over the course of a year.
12⋅12=144stamps
By adding the new stamps to the stamps she already has, which is 120 stamps, we get her total number of stamps at the end of the year.
120+144=264stamps
c The total stamps she has after n months is labeled t(n). In n months she will receive 12n stamps.
t(n)=12n
To 12n, we also have to add the stamps she already had to get the total number of stamps she owns in any given month.
t(n)=12n+120
d We want to determine n for which t(n)=500. Let's substitute this in our equation and solve for n.
After 31.67 months she will have received 500 stamps. However, Lona does not receive new stamps until the end of the month. Therefore, she does not receive them one at the time, but in batches of 12. As a result, we can say that her total number of stamps will never be exactly 500. During month 31, the number of stamps will be less than 500 and during month 32 it will be greater. Therefore, in month 32, the book will be filled with a few stamps leftover.
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