Tiffany is monitoring the decay of two radioactive compounds in test tubes at her lab. Compound A is continuously decaying at a rate of 12% and compound B is continuously decaying at a rate of 18%. Tiffany started with 30 grams of compound A and 40 grams of compound B.
Create a system of inequalities that can be used to determine when both compounds will be less than or equal to the same mass, M, where t is time, in weeks, P_(A) is the initial amount of compound A, P_(B)
is the initial amount of compound B, and r is the rate of decay. Enter the inequalities in the field by replacing the values of P_(A),P_(B), and r.
P(base A)e^rt≤M
P(base B)e^rt≤M
The system of inequalities can be stated as:
P_(A)e^(0.12t) ≤ M
P_(B)e^(0.18t) ≤ M