Question

A drug loses decayrate percent of its potency every month. Also, a drug is considered expired if it loses more than 50% potency. Write a function calculate (months, decayrate) that returns the potency, thus this function must have the calculations. Your goal is to write a boolean function IsExpired (potency) that returns True if the drug has expired and False if it has not. Example 1: calculate (10,10) returns 34.87 Is Expired (34.87) should return True. Explanation: The drug loses 10% potency every month. After 1st month the potency 90%, after 2nd month its 81%. In this way, after 7th month the potency is 47.83%. Example 2: calculate (15,4.5) return 50.12 Is Expired (50.12) should return False. Explanation: After 15th month the drug still has 50.12% potency.

Answer 1

The time it takes for 90% of the iodine-131 to decay can be calculated using the first-order decay equation, substituting 0.10 for the ratio of A/A0 and using the given decay constant of 0.138 d⁻¹.

Step-by-step explanation:

To determine the time required for 90% of the iodine-131 in a 0.500 M solution to decay to Xe-131, we can use the first-order decay equation. The decay of iodine-131 is a first-order process, characterized by a decay constant (λ) which is given as 0.138 d⁻¹. For a first-order decay, the relationship between the remaining concentration (A) of a substance and time (t) can be described by the equation:

A = A₀e⁻λt

Where A₀ is the initial concentration and e is the base of the natural logarithm. Since we are looking for the time it takes for the substance to decay to 10% of its original concentration (90% decay), we can set A/A₀ to 0.10.

0.10 = e⁻λt
Taking the natural logarithm of both sides gives:
ln(0.10) = -λt
Solving for t:
t = -ln(0.10) / λ

Substituting the given decay constant (0.138 d⁻¹), we get:

t = -ln(0.10) / 0.138