precalculus, math, intrest, algerbra 2

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

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asked by charlie
  1. The card was originally $1. Please help find the effective yield

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    posted by charlie
  2. 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

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    posted by Reiny

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