Question

1. Stanley started a basketball card collection with 11 cards that he received

as a gift from his grandfather.
He purchased one pack of cards every month for 15 years. After one year,
he had a total of 107 cards in his collection.
Stanley donated his entire collection 15 years after he got it from his
grandfather.
What is the domain of the function representing the number of basketball
cards in Stanley's collection.?

Answer 1

see the explanation

Explanation:

Let

c------> the number of cards in one pack of cards

we know that

After one year, he had a total of 107 cards in his collection.

Remember that in one year there are 12 months

so

107=12c+11

Solve for c

12c=107-11

12c=96

c=96/12

c=8 cards

One pack has 8 cards

Let

x ------> the time in months

f(x) ------> the number of basketball cards in Stanley's collection

The linear equation that represent this situation is

f(x)=8x+11

Find out the number of cards after 15 years

x=15*12=180 months

substitute

f(180)=8(180)+11=1,451 cards

therefore

The domain of the function is 180 months

The range of the function is 1,451 cards