Question

A patient ingests 5 grams of a certain drug which dissolves away at a constant rate of 10% per hour.How long will it take before there is only one gram left?

a.)15.9 hours
b.)14.2 hours
c.)15.3 hours
d.)16.9 hours

Answer 1

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.