7-18. tn 1999, Chartie received the family heidloom marble collection consisting

Question

7-18. tn 1999, Chartie received the family heidloom marble collection consisting of eat grandfather had adkled the sae e namber of martdes per year to 1230 marbles, collection in 1905. Each year, Charlie's g mumber of maubles to his collection. When he passed them on to his son, he Charlie's great grandfather had started the original martbe insisted that each future generation add the san the collection. When Charlie's father eceived the collection in 166, there were 810 martles liy the time Charice nsherited the colection,foer how many years hal been in existence? a b. How many marbles are akled to the collection exch year? were in the original collection when Charlie's great-grandfather started it. d. Geacralize this situation by writing a function describing the growth of the marble collesction for each year (n) since Charlie's great grandfather started it. How old will the marble collection be when Charlie (or one of his children) has moe than 2000 marbles? In what year will this occur? e. 7-19, Copy and conmplete each of the Diamond Problems below The pattern wsed in the Diamond Problems is shown at right. b, d.

Explanation / Answer

a) from 1905 to 1999 the time elapsed = 1999 - 1905

= 94 years

b) from 1966 to 1999 marbles added were 1239 - 810 = 429 marbles

429 / 33 = 13

so 13 marbles per year were added

c) the linear equation becomes

y = 13x + b

where 13 is the number of marbles each year

plugging y = 1239 and x = 94

we get , b = 17

hence, charlies great grandfather started it at 17 marbles

d) the function can be written as

M (n) = 13n + 17

e) when charlie has more that 2000 marbles

2000 = 13n + 17

n = 153

it will be 153 years old

it will happen in the year 1905 + 153 = year 2058

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