Question

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. kodi looking into his box of baseball cards. how many cards were in the original box? is this t(0) or t(1)? write the first few terms of the sequence. kodi plans to keep the collection for a long time. how many cards will the collection contain 10 years from now? write an equation that determines the number of cards in the collection after n years. what does each number in your rule represent?

Answer 1

(3,52)(7,108)
slope = (108 - 52) / (7 - 3) = 56/4 = 14

y = mx + b
slope(m) = 14
(3,52)...x = 3 and y = 52
sub and find b, the y int (the original amount of cards)
52 = 3(14) + b
52 = 42 + b
52 - 42 = b
10 = b

so ur equation is y = 14x + 10....with x being the number of years and y being the total cards. <== ur equation is y = 14x + 10

He started with 10 cards....and has been adding 14 cards every year.

so after 10 years...
y = 14(10) + 10
y = 140 + 10
y = 150 <== after 10 years, he will have 150 cards