A tumor is injected with 0.82 grams of Iodine-125. After 1 day, the amount of Iodine- 125 has decreased by $1.15 \%$.

Write an exponential decay model with $A(t)$ representing the amount of Iodine- 125 remaining in the tumor after $t$ days. Enclose arguments of the function in parentheses and include a multiplication sign between terms. For example, $c^{*} \ln (t)$.

Then use the formula for $A(t)$ to find the amount of Iodine-125 that would remain in the tumor after 8.5 days. Round your answer to the nearest thousandth ( 3 decimal places) of a gram.

Step 1 ：Given that a tumor is injected with 0.82 grams of Iodine-125 and after 1 day, the amount of Iodine-125 has decreased by $1.15 \%$. We are asked to write an exponential decay model with $A(t)$ representing the amount of Iodine-125 remaining in the tumor after $t$ days and then use the formula for $A(t)$ to find the amount of Iodine-125 that would remain in the tumor after 8.5 days.

Step 2 ：The exponential decay model is given by the formula $A(t) = A_0 * e^{kt}$, where $A_0$ is the initial amount, $k$ is the decay constant, and $t$ is the time.

Step 3 ：In this case, $A_0$ is 0.82 grams, $t$ is 1 day, and the amount of Iodine-125 has decreased by $1.15 \%$, so $A(t)$ is $0.82 * (1 - 0.0115) = 0.81$ grams.

Step 4 ：We can solve for $k$ using the formula $k = \frac{1}{t} \ln \left( \frac{A(t)}{A_0} \right)$. Substituting the given values, we get $k = -0.011566636371465405$.

Step 5 ：Once we have $k$, we can use the formula for $A(t)$ to find the amount of Iodine-125 that would remain in the tumor after 8.5 days. Substituting the values, we get $A(8.5) = 0.743$ grams.

Step 6 ：Final Answer: The amount of Iodine-125 that would remain in the tumor after 8.5 days is \(\boxed{0.743}\) grams.