A tumor is injected with 3.5 grams of lodine, which has a decay rate of $1.15 \%$ per day.
Write an exponential model representing the amount of lodine remaining in the tumor after $t$ days. Find the amount of lodine that would remain in the tumor after 60 days. Round to the nearest tenth of a gram.
Answer
Round the final answer to the nearest tenth of a gram to get \(\boxed{1.7}\) grams.
Step 1 ：Given that a tumor is injected with 3.5 grams of lodine, which has a decay rate of 1.15% per day.
Step 2 ：We can write an exponential model representing the amount of lodine remaining in the tumor after \(t\) days using the formula \(A = P(1 - r)^t\), where \(A\) is the final amount, \(P\) is the initial amount, \(r\) is the decay rate, and \(t\) is the time.
Step 3 ：In this case, \(P = 3.5\) grams, \(r = 1.15\% = 0.0115\), and \(t = 60\) days.
Step 4 ：Substitute these values into the formula to find the amount of lodine remaining after 60 days: \(A = 3.5(1 - 0.0115)^{60}\)
Step 5 ：Calculate the above expression to get the final amount of lodine remaining in the tumor after 60 days, which is approximately 1.7485113804747696 grams.
Step 6 ：Round the final answer to the nearest tenth of a gram to get \(\boxed{1.7}\) grams.
