Question

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.

Answer 1

You are missing information here.

The way it is worded we would have to know what the initial value of the card was.

I would use the equation
Value = a(10)^(t/9) where a is the initial value, and t is the number of years

32 = a(10^(t/9)

t/9 = log(32/a) / log 10

t/9 = log(32/a) because log 10 = 1

once you have a, you can finish it.

Answer 2

wait I forgot to add that she bought the card origionally for $1

Answer 3

then as I said replace a with 1 in

t/9 = log(32/a) to get
t = 9log32
= 13.55 years