Type the correct answer in the box.
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.
Let M represent the mass at which both compounds will be less than or equal to.
The decay equation for compound A can be represented as:
P_(A) - r * P_(A) * t ≤ M
The decay equation for compound B can be represented as:
P_(B) - r * P_(B) * t ≤ M
Replacing the values, the system of inequalities becomes:
30 - 0.12 * 30 * t ≤ M
40 - 0.18 * 40 * t ≤ M