SOLUTION: Seven years ago, Kodi found a box of old baseball cards in the garage. Since then, he has added a consistent number of cards to the collection each year. He had 52 cards in the col

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Question 159248: Seven years ago, Kodi found a box of old baseball cards in the garage. Since then, he has added a consistent number of cards to the collection each year. He had 52 cards in the colection after 3 years and now has 108 cards.
How many cards were in the original box?
Kodi plans to keep the collection for a long time. How many cards will the collection contain 10 years from now?
Write a rules that determines the number of cards in the collection after n years. What does each number in your rule represent?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Seven years ago, Kodi found a box of old baseball cards in the garage. Since then, he has added a consistent number of cards to the collection each year. He had 52 cards in the collection after 3 years and now has 108 cards.
How many cards were in the original box?
:
The information given can be summarized:
After 3 yrs, he had 52 cards
After 7 yrs, he had 108 cards
:
Assign these values as follows:
x1 = 3; y1 = 52
x2 = 7; y2 = 108
:
Find the slope; m = %28%28y2-y1%29%29%2F%28%28x2-x1%29%29
;
m = %28%28108-52%29%29%2F%28%287-3%29%29 = 56%2F4 = 14 is the slope
;
Find the equation using the point/slope equation: y - y1 = m(x- x1)
y - 52 = 14(x - 3)
y - 52 = 14x - 42
y = 14x - 42 + 52
y = 14x + 10
:
"How many cards were in the original box?"
7 years ago x = 0, from the equation we can see that y = 10
:
:
Kodi plans to keep the collection for a long time. How many cards will the collection contain 10 years from now?
:
Substitute 10 for x in our equation
y = 14(10) + 10
y = 150 cards in 10 years:
:
Write a rules that determines the number of cards in the collection after n years.
We can translate our equation to:
No. of cards = 14n + 10
:
What does each number in your rule represent?
For each increase in n we have 14 more cards