My investment in Edgewater stocks is losing half its value every 2 years. Find and interpret the associated decay rate.

If I use the formula y=100(1/2)^x (<-- Is that correct?)

I got the answer of 0% (its wrong), I used a different formula, which should be wrong and got the answer of 25% and 34%

Is that the formula to solve the equation? Why is it wrong? How should I solve it?

Thank you

25

To find the associated decay rate for an investment that loses half its value every 2 years, you can use the formula:

y = a(1/2)^(x/t),

where:
y is the final value of the investment,
a is the initial value of the investment,
x is the number of years passed, and
t is the time it takes for the investment to lose half its value.

In this case, the initial value of the investment is not given, so let's use a = 100 for the sake of calculation. The time it takes for the investment to lose half its value is given as 2 years.

So, the formula becomes:

y = 100(1/2)^(x/2).

Now, let's interpret the decay rate. The decay rate can be found by observing how the investment decreases in value over time. It represents the percentage by which the investment decreases in value per unit of time.

Let's calculate the value of the investment after 2 years (x = 2):

y = 100(1/2)^(2/2)
= 100(1/2)^1
= 100(1/2)
= 50.

So, the investment will be worth 50 after 2 years.

To find the decay rate, you can calculate the percentage decrease in value over 2 years. Start with the initial value (a = 100) and subtract the final value (y = 50). Then, divide the difference by the initial value and multiply by 100 to get the percentage:

decay rate = ((a - y) / a) * 100
= ((100 - 50) / 100) * 100
= (50 / 100) * 100
= 50%.

Therefore, the associated decay rate for this investment is 50%. This means that the investment loses 50% of its value every 2 years.

The formula you initially used, y = 100(1/2)^x, is not appropriate for this scenario because it does not account for the specific time it takes for the investment to lose half its value. By adjusting the formula to include the time factor, you can accurately calculate the decay rate and interpret the results correctly.