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

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

To estimate the effective yield of an investment in the basketball card, we need to calculate the percentage increase in value per year.

Since the card's value increases by a factor of 10 every 9 years, we can calculate the approximate annual growth rate by finding the 9th root of 10.

Using a calculator or an online tool, we find that the 9th root of 10 is approximately 1.257.

To determine the effective annual yield, we subtract 1 from this value (1.257 - 1 = 0.257) and then convert it to a percentage by multiplying by 100.

Therefore, the estimated effective yield of the investment in the basketball card is approximately 25.7%.