Answer :
To determine the percentage of carbon-14 remaining in an object after 55 years, given the decay function \(C(t) = 100 \cdot e^{-0.000121 t}\), we can follow these steps:
1. Identify the given function and variables:
- The function is \(C(t) = 100 \cdot e^{-0.000121 t}\).
- We need to find \(C(t)\) when \(t = 55\) years.
- The decay constant is \(-0.000121\).
2. Substitute \(t = 55\) into the function:
[tex]\[ C(55) = 100 \cdot e^{-0.000121 \times 55} \][/tex]
3. Calculate the exponent:
[tex]\[ -0.000121 \times 55 = -0.006655 \][/tex]
4. Compute the value of \(e^{-0.006655}\):
- Using a calculator or an appropriate method, we find the value of the exponential function. Let us denote this value by \(e^{-0.006655}\).
5. Multiply by the initial amount 100:
[tex]\[ C(55) = 100 \cdot e^{-0.006655} \][/tex]
6. Round the final result to the nearest hundredth:
After performing the calculations, the rounded value of \(C(55)\) is approximately \(99.34\).
So, the percentage of carbon-14 remaining in the object after 55 years is:
[tex]\[ C(55) \approx 99.34\% \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{99.34} \][/tex]
Therefore, the percentage of carbon-14 remaining in the object after 55 years is \(99.34\%\).
Hence, the correct choice is [tex]\( \mathbf{B. \, 99.34} \)[/tex].
1. Identify the given function and variables:
- The function is \(C(t) = 100 \cdot e^{-0.000121 t}\).
- We need to find \(C(t)\) when \(t = 55\) years.
- The decay constant is \(-0.000121\).
2. Substitute \(t = 55\) into the function:
[tex]\[ C(55) = 100 \cdot e^{-0.000121 \times 55} \][/tex]
3. Calculate the exponent:
[tex]\[ -0.000121 \times 55 = -0.006655 \][/tex]
4. Compute the value of \(e^{-0.006655}\):
- Using a calculator or an appropriate method, we find the value of the exponential function. Let us denote this value by \(e^{-0.006655}\).
5. Multiply by the initial amount 100:
[tex]\[ C(55) = 100 \cdot e^{-0.006655} \][/tex]
6. Round the final result to the nearest hundredth:
After performing the calculations, the rounded value of \(C(55)\) is approximately \(99.34\).
So, the percentage of carbon-14 remaining in the object after 55 years is:
[tex]\[ C(55) \approx 99.34\% \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{99.34} \][/tex]
Therefore, the percentage of carbon-14 remaining in the object after 55 years is \(99.34\%\).
Hence, the correct choice is [tex]\( \mathbf{B. \, 99.34} \)[/tex].
