If after two hours,0.9Ao remains, how can I find k
To answer this question, we need to know more details about the problem. Can you please provide more information about what Ao and k represent and any other relevant information provided in the problem?
To find the value of k, we need to use the exponential decay equation, which is given as:
A = A0 * e^(-kt)
Where:
- A is the final amount remaining after time t
- A0 is the initial amount
- k is the decay constant
- t is the time
In your case, we have:
A = 0.9Ao (as given)
t = 2 hours (as given)
Substituting these values into the equation, we get:
0.9Ao = A0 * e^(-2k)
To find the value of k, we need more information. Specifically, we need the initial amount A0, which is missing in the given information. Can you provide the initial amount (A0)?
To find the value of k, we need to use the exponential decay formula. The formula for exponential decay is:
A = A₀ * e^(-kt)
Where:
A is the remaining quantity after time t.
A₀ is the initial quantity.
k is the decay constant.
t is the time elapsed.
In this case, we are given that after two hours, 0.9 times the initial quantity (Ao) remains. So, we can write the equation as:
0.9Ao = Ao * e^(-2k)
To solve for k, we need to isolate it on one side of the equation. We can divide both sides of the equation by Ao:
0.9 = e^(-2k)
Next, we need to take the natural logarithm (ln) of both sides to eliminate the exponential term:
ln(0.9) = ln(e^(-2k))
The natural logarithm of e is 1, so we can simplify further:
ln(0.9) = -2k
Finally, we can solve for k by dividing both sides of the equation by -2:
k = ln(0.9) / -2
Using a calculator or a math software, evaluate ln(0.9) and divide it by -2 to find the value of k.