At the show a basketball card dealer tells you that a vintage card increases in value by a factor of 10 every 9 years.If the card is now worth $32, how long ago did she buy it?(Hint: Remember that the value is multiplied by 10 every 9 years, not every year.)
2nd Question
Estimate the effective yield of an investiment in this basketball card.
I Just need the answer for number 2
2 answers
The card was originally $1. Please help find the effective yield
value = 1(10)^(t/9)
so when value = 32
32 = 10^(t/9)
take log ob both sides
log 32 = (t/9) log 10 , using basic log rules, but log10 = 1
t/9 = log32
t = 9log32 = appr 13.5 years
at end of 1 year
value = 10^(1/9) = 1.2915..
so the effective rate = appr 29.15%
check: 1.291549665..^(13.5463498.../9) = 32
so when value = 32
32 = 10^(t/9)
take log ob both sides
log 32 = (t/9) log 10 , using basic log rules, but log10 = 1
t/9 = log32
t = 9log32 = appr 13.5 years
at end of 1 year
value = 10^(1/9) = 1.2915..
so the effective rate = appr 29.15%
check: 1.291549665..^(13.5463498.../9) = 32