Question

A collector's hockey card is purchased in 1990 for $5. The value increases by 6% every year. a) Write an equation that models the value of the card, given the number of years since 1990. b) Determine the increases in value of the card in the 4th year after it was purchased (from yr 3 to yr4) c) Determine the increases in value of the card in the 20th year after it was purchased.
the answer ifor b is 0.36.... i just dont know how they got that

Answer 1

so what do yo think?

Answer 2

you*

Answer 3

Do you know the general formula for growth?

Answer 4

y=5(1.06)^x

Answer 5

And you just answered your part a.

Answer 6

yep, i just need part b and c

Answer 7

the answer for b is 0.36
how did the book get that?

Answer 8

You can look at the first couple years to establish a pattern. In 1991 (1 year after 1990), The worth of the card is 5*1.06.

In 1992 (2 years after 1990), the worth of the card is 5*1.06*1.06, or
5(1.06)2

After 3 years, it's
5(1.06)3

After n years, it's
5(1.06)n

Answer 9

i tried that for year 3, but i got $5.95

Answer 10

Oh, I think I know, here, subtract these values:
\[\LARGE (5(1.04^4)-(5(1.04^3)\]

Answer 11

YEA! IT WORKED

Answer 12

THANKS!! what about part c

Answer 13

I think it's just asking how much higher the price was during year 20 compared to the original:
\[\LARGE (5(1.04)^{20})-5\]
Solve that and that should give you your answer.

Answer 14

I got 11.03

Answer 15

the answer is 0.95

Answer 16

and the growth rate is 1.06 not 1.04

Answer 17

Try:
\[\LARGE (5(1.06)^{20})-(5(1.06^{19})\]
Whoops, my mistake.

Answer 18

close, the answer is 0.91

Answer 19

but why would you think to subtract year 20 and year 19? im just wondering

Answer 20

Well that's all I got. I'm just assuming that it's similar to part b.

Answer 21

ahh, okay

Answer 22

Yea, sorry. I don't have any more ideas on what to do with part c.

Answer 23

thats okay thanks :)

Answer 24

Anytime~