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Answer :
To find out how much of the radioactive compound will remain after 5 hours, we need to use the formula for exponential decay, which is:
[tex]\[ C = P \times (1 - r)^t \][/tex]
Where:
- [tex]\( C \)[/tex] is the remaining amount.
- [tex]\( P \)[/tex] is the initial amount, which is 360 grams.
- [tex]\( r \)[/tex] is the decay rate, which is 3% or 0.03.
- [tex]\( t \)[/tex] is the time in hours, which is 5 in this case.
Let's go through the steps:
1. Substitute the initial mass ([tex]\( P \)[/tex]), the decay rate ([tex]\( r \)[/tex]), and the time ([tex]\( t \)[/tex]) into the formula:
[tex]\[
C = 360 \times (1 - 0.03)^5
\][/tex]
2. Perform the subtraction within the parentheses:
[tex]\[
1 - 0.03 = 0.97
\][/tex]
3. Raise the result to the power of the time, which is 5:
[tex]\[
0.97^5 \approx 0.858734025
\][/tex]
4. Multiply the initial mass by the result of the previous calculation:
[tex]\[
C = 360 \times 0.858734025 \approx 309.144
\][/tex]
So, approximately 309.144 grams of the compound will remain after 5 hours.
Thus, the correct equation that represents how many grams of the compound will remain after 5 hours is:
[tex]\[ C = 360 \times (0.97)^5 \][/tex]
The correct answer is C. [tex]\( C=360(0.97)^5 \)[/tex].
[tex]\[ C = P \times (1 - r)^t \][/tex]
Where:
- [tex]\( C \)[/tex] is the remaining amount.
- [tex]\( P \)[/tex] is the initial amount, which is 360 grams.
- [tex]\( r \)[/tex] is the decay rate, which is 3% or 0.03.
- [tex]\( t \)[/tex] is the time in hours, which is 5 in this case.
Let's go through the steps:
1. Substitute the initial mass ([tex]\( P \)[/tex]), the decay rate ([tex]\( r \)[/tex]), and the time ([tex]\( t \)[/tex]) into the formula:
[tex]\[
C = 360 \times (1 - 0.03)^5
\][/tex]
2. Perform the subtraction within the parentheses:
[tex]\[
1 - 0.03 = 0.97
\][/tex]
3. Raise the result to the power of the time, which is 5:
[tex]\[
0.97^5 \approx 0.858734025
\][/tex]
4. Multiply the initial mass by the result of the previous calculation:
[tex]\[
C = 360 \times 0.858734025 \approx 309.144
\][/tex]
So, approximately 309.144 grams of the compound will remain after 5 hours.
Thus, the correct equation that represents how many grams of the compound will remain after 5 hours is:
[tex]\[ C = 360 \times (0.97)^5 \][/tex]
The correct answer is C. [tex]\( C=360(0.97)^5 \)[/tex].
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