My investment in website #1 stocks is losing half its value every 2 years. Find and interpret the associated decay rate.
Round your answer to one decimal place.
How do i find this? Do I use the half-life formula? Because I got it wrong I got 25%
Thank you
To find the decay rate associated with your investment, you can use the half-life formula. However, in this case, the half-life formula might not lead to the correct answer since the value is decreasing by half every 2 years, rather than a regular half-life scenario.
Instead, you can use a different formula to find the decay rate. The formula for exponential decay is:
A = A0 * e^(kt),
where A0 is the initial value, A is the final value, t is the time period, k is the decay constant, and e is Euler's number (approximately 2.71828).
In this case, since the initial value is being halved every 2 years, we can use the formula:
0.5A0 = A0 * e^(2k).
Dividing both sides of the equation by A0, we get:
0.5 = e^(2k).
To solve for k, take the natural logarithm (ln) of both sides of the equation:
ln(0.5) = 2k * ln(e).
Since ln(e) equals 1, the equation simplifies to:
ln(0.5) = 2k.
Now, solve for k by dividing both sides of the equation by 2:
k = ln(0.5) / 2.
Using a calculator, you can find the value of k, which will represent the decay rate associated with your investment in website #1 stocks.