Final answer:
To determine the time it will take for 5 grams of a drug to decay to 1 gram at a constant rate of 10% per hour, the exponential decay formula A = P(1 - r)^t is used and logarithms are applied to solve for time t.
Step-by-step explanation:
The student's question relates to the exponential decay of a drug in the body. Specifically, we are looking at the time it will take for a 5-gram sample of a drug to decay to 1 gram at a constant rate of 10% per hour. Using the concept of exponential decay, the formula to find the remaining amount after a certain number of hours is:
A = P(1 - r)^t
Where:
- A is the amount remaining after time t
- P is the initial amount (5 grams in this case)
- r is the decay rate (0.10 for 10%)
- t is the time in hours
We need to solve for t when A is 1 gram.
1 = 5(1 - 0.10)^t
0.2 = (0.9)^t
Using the logarithm to solve for t:
log(0.2) = log((0.9)^t)
log(0.2) = t * log(0.9)
t = log(0.2) / log(0.9)
Calculating the above expression will give the time t in hours before there is only 1 gram of the drug left in the body.