Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Type the correct answer in the box.

Tiffany is monitoring the decay of two radioactive compounds in test tubes at her lab. Compound [tex]$A$[/tex] is continuously decaying at a rate of [tex]$12\%$[/tex] and compound [tex]$B$[/tex] is continuously decaying at a rate of [tex]$18\%$[/tex]. Tiffany started with 30 grams of compound [tex]$A$[/tex] and 40 grams of compound [tex]$B$[/tex].

Create a system of inequalities that can be used to determine when both compounds will be less than or equal to the same mass, [tex]$M$[/tex], where [tex]$t$[/tex] is time in weeks, [tex]$P_A$[/tex] is the initial amount of compound [tex]$A$[/tex], [tex]$P_B$[/tex] is the initial amount of compound [tex]$B$[/tex], and [tex]$r$[/tex] is the rate of decay.

Enter the inequalities in the field by replacing the values of [tex]$P_A$[/tex], [tex]$P_B$[/tex], and [tex]$r$[/tex].

[tex]\[30 e^{-0.12 t} \leq M\][/tex]
[tex]\[40 e^{-0.18 t} \leq M\][/tex]

Sagot :

GinnyAnswer
Tiffany starts with 30 grams of compound [tex]$A$[/tex] and 40 grams of compound [tex]$B$[/tex].

The decay rates are:
- Compound [tex]$A$[/tex]: 12% per week
- Compound [tex]$B$[/tex]: 18% per week

This gives:
- [tex]\( P_A = 30 \)[/tex]
- [tex]\( P_B = 40 \)[/tex]
- [tex]\( r_A = -0.12 \)[/tex]
- [tex]\( r_B = -0.18 \)[/tex]

The general form of the inequalities is:
[tex]\[ P_A e^{r_A t} \leq M \][/tex]
[tex]\[ P_B e^{r_B t} \leq M \][/tex]

Plugging in the values, we get:
[tex]\[ 30 e^{-0.12 t} \leq M \][/tex]
[tex]\[ 40 e^{-0.18 t} \leq M \][/tex]

So, the system of inequalities is:
[tex]\[ 30 e^{-0.12 t} \leq M \][/tex]
[tex]\[ 40 e^{-0.18 t} \leq M \][/tex]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.