Question

"If 100mg of a drug dissolves at a rate of 20% per hour, how long will it take for there to be only 10mg left?

a) 1 hour
b) 2 hours
c) 3 hours
d) 4 hours"

Answer 1

To determine the time it will take for only 10mg of a drug to remain from an initial amount of 100mg, decaying at a rate of 20% per hour, we use the exponential decay formula. The calculation shows it will take approximately 4 hours for the amount to reduce to 10mg.

Step-by-step explanation:

The student asked: "If 100mg of a drug dissolves at a rate of 20% per hour, how long will it take for there to be only 10mg left?" To solve this, we need to understand the concept of an exponential decay process. This scenario describes a drug losing its mass at a constant percentage rate, which is a common example of exponential decay in mathematics. A drug dissolving at 20% per hour means that each hour, the drug's remaining amount is 80% of the amount at the beginning of that hour.

Using the formula for exponential decay, A = P(1-r)^t where:

10 = 100(1-0.2)^t
Solve for t:
0.1 = (0.8)^t
Taking the logarithm of both sides gives:
log(0.1) = t * log(0.8)
t = log(0.1) / log(0.8)
Calculate t, and you'll find t is approximately 4 hours. So, the correct answer is (d) 4 hours.