Evaluating an exponential function that models a real-world... following exponential function.
\[
A(t)=381\left(\frac{1}{2}\right)^{\frac{t}{30}}
\]
Find the amount of the sample remaining after 40 years and after 80 years. Round your answers to the nearest gram as necessary.
Amount after 40 years:
Answer
\boxed{\text{Final Answer: The amount of the sample remaining after 40 years is 151 grams, and after 80 years, it is 60 grams.}}
Step 1 ：Plug in t = 40 and t = 80 into the given exponential function: \(A(40)=381\left(\frac{1}{2}\right)^{\frac{40}{30}}\) and \(A(80)=381\left(\frac{1}{2}\right)^{\frac{80}{30}}\)
Step 2 ：Calculate the results: \(A(40) \approx 151\) grams and \(A(80) \approx 60\) grams
Step 3 ：\boxed{\text{Final Answer: The amount of the sample remaining after 40 years is 151 grams, and after 80 years, it is 60 grams.}}
