Answered

IDNLearn.com is your go-to platform for finding reliable answers quickly. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.

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 :

GinnyAnsweridn
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]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.