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.)

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

then as I said replace a with 1 in

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

Answer 2

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 3

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

Answer 4

To find out how long ago the card dealer bought the card, we can use the fact that the value of the card multiplied by 10 every 9 years.

Let's set up an equation to solve for the number of periods (years) it took for the card to increase in value to $32:

Starting value: $1 (since the question mentions a factor of 10 increase)
Value after n periods: $32
Factor of increase per period: 10

Using exponential growth, the equation can be written as:

$1 * (10)^n = $32

To solve for n, we need to take the logarithm (base 10) of both sides of the equation:

log10($1 * (10)^n) = log10($32)
log10($1) + log10(10)^n = log10($32)
0 + n * log10(10) = log10($32)
n = log10($32) / log10(10)

Now we can use a calculator to find the value of n:

n ≈ 1.505

Therefore, it took approximately 1.505 periods of 9 years for the card to increase in value to $32. To find out how long ago the dealer bought the card, we simply multiply the number of periods by 9 years:

Time ago = n * 9 years ≈ 1.505 * 9 years ≈ 13.545 years

So, the card dealer bought the card approximately 13.545 years ago.

For the second question, we need more information about the initial investment, any additional costs, and potential final selling price to calculate the effective yield.