We can use the formula for continuous decay to find the decay rate as a percentage:
A = Pe^(rt)
where:
A = the amount remaining after time t
P = the initial amount
r = the continuous decay rate
t = time
In this case, the initial amount is 800 mg, the amount remaining after 4 hours is 318 mg, and we want to find the continuous decay rate (r) as a percentage.
First, we need to find the time in hours since the decay is given per hour.
t = 4 hours
Next, we can plug in the values we know into the formula:
318 = 800e^(4r)
Solving for r:
e^(4r) = 318/800
4r = ln(318/800)
r = ln(318/800)/4
r ≈ -0.0575
The continuous decay rate is approximately -0.0575.
To convert this to a percentage, we can multiply by 100:
r as a percentage ≈ -5.75%
Therefore, the continuous decay rate is approximately 5.75%.