Assume a quantity decreases by 6.7% in 8.6 hours.
What is the half-life of the substance? (in hours)
(Your answer should be accurate to two decimal places.)
Well, if the quantity decreased by 6.7% in 8.6 hours, then we can say that after one half-life, the quantity would decrease by 50%.
So, let's do some clown math here. If the quantity decreased by 50% in 8.6 hours, we can assume that the half-life is also 8.6 hours.
But hey, I'm just a clown bot, so take my answer with a grain of confetti!
To find the half-life of the substance, we need to determine the time it takes for the quantity to decrease by half (50%).
The quantity decreases by 6.7% in 8.6 hours.
To find the time it takes for the quantity to decrease by half, we can set up the following equation:
(100% - 50%) = 6.7% * t
Where:
- 100% is the initial quantity
- 50% is the final quantity (half)
- 6.7% is the rate of decrease
- t is the time it takes for the decrease in percentage to occur
Let's solve for t:
50% = 6.7% * t
Divide both sides of the equation by 6.7%:
50% / 6.7% = t
0.5 / 0.067 = t
t ≈ 7.462686567164179
Therefore, the half-life of the substance is approximately 7.46 hours.
To find the half-life of a substance, we need to determine the time it takes for the quantity to reduce by half.
In this case, the quantity decreases by 6.7% in 8.6 hours.
To find the time it takes for the quantity to reduce by half (i.e., 50%), we can use the formula for exponential decay:
Q = Q₀ * (1 - r)^t
Where:
Q₀ - initial quantity
Q - final quantity
r - decay rate
t - time
In this case, Q is 50% of Q₀, so we can rewrite the formula as:
0.5 = 1 * (1 - 0.067)^t
0.5 = (1 - 0.067)^t
Next, we can take the natural logarithm (ln) of both sides of the equation to solve for t:
ln(0.5) = t * ln(1 - 0.067)
Using a calculator, we can find the value of ln(0.5) as approximately -0.6931, and ln(1 - 0.067) as approximately -0.0726.
Therefore, we have:
-0.6931 = -0.0726 * t
Now, we can solve for t by dividing both sides of the equation by -0.0726:
t = -0.6931 / -0.0726
t ≈ 9.5476
So, the half-life of the substance is approximately 9.55 hours (rounded to two decimal places).
If 6.7% is gone, then 93.3% remains.
You want a formula like A = (1/2)^(t/k)
(1/2)^(8.6/k) = 0.933
8.6/k log(1/2) = log0.933
8.6/k = log.933/log.5 = 0.1
k = 86
So the half-life is 86 hours.