Questions: After an injection, the amount of a medication A, in cubic centimeters (cc), in the bloodstream decreases with time t, in hours. Suppose that under certain conditions A is given by the function below, where A0 is the initial amount of the medication. Assume that an initial amount of 90 cc is injected. Complete parts (a) through (d). A(t)= A0 / (t^2 + 1) a) Find A(0), A(1), A(2), A(8), and A(10). A(0)=90.0000

Solution Steps

To solve this problem, we need to evaluate the function \( A(t) = \frac{A_0}{t^2 + 1} \) at specific values of \( t \). Given that the initial amount \( A_0 \) is 90 cc, we will substitute \( t = 0, 1, 2, 8, \) and \( 10 \) into the function to find the corresponding values of \( A(t) \).

To find \( A(0) \), we substitute \( t = 0 \) into the function: \[ A(0) = \frac{90}{0^2 + 1} = \frac{90}{1} = 90.0000 \]

Next, we calculate \( A(1) \): \[ A(1) = \frac{90}{1^2 + 1} = \frac{90}{2} = 45.0000 \]

Now, we find \( A(2) \): \[ A(2) = \frac{90}{2^2 + 1} = \frac{90}{4 + 1} = \frac{90}{5} = 18.0000 \]

Next, we calculate \( A(8) \): \[ A(8) = \frac{90}{8^2 + 1} = \frac{90}{64 + 1} = \frac{90}{65} \approx 1.3846 \]

Finally, we find \( A(10) \): \[ A(10) = \frac{90}{10^2 + 1} = \frac{90}{100 + 1} = \frac{90}{101} \approx 0.8911 \]

Final Answer