type the correct answer in the box. tiffany is monitoring the decay of two radioactive compounds in test…

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. $p_ae^{rt}leq m$ $p_be^{rt}leq m$

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. $p_ae^{rt}leq m$ $p_be^{rt}leq m$

Answer

Explanation:

Step1: Identify values for compound A

Given $P_A = 30$ (initial amount of compound A) and $r=- 0.12$ (12% decay rate, so negative). Substitute into decay formula $P_Ae^{rt}\leq M$. $30e^{-0.12t}\leq M$

Step2: Identify values for compound B

Given $P_B = 40$ (initial amount of compound B) and $r = - 0.18$ (18% decay rate, so negative). Substitute into decay formula $P_Be^{rt}\leq M$. $40e^{-0.18t}\leq M$

Answer:

$30e^{-0.12t}\leq M$, $40e^{-0.18t}\leq M$