Question

Radium-226, in grams, decays in such a way that after t years, the amount left over can be modeled by the equation A(t)=450e−0.0004t
. How many grams of Radium-226 will remain after seven years? Round your answer to the nearest tenth.(1 point)

Answer 1

To find the amount of Radium-226 remaining after 7 years using the equation \( A(t) = 450e^{-0.0004t} \), we substitute \( t = 7 \) into the equation.

\[
A(7) = 450e^{-0.0004 \times 7}
\]

First, we calculate \( -0.0004 \times 7 \):

\[
-0.0004 \times 7 = -0.0028
\]

Next, we compute the value of \( e^{-0.0028} \):

\[
e^{-0.0028} \approx 0.9972 \quad (\text{using a calculator or exponent table})
\]

Now substituting this value back into the equation:

\[
A(7) = 450 \times 0.9972
\]

Calculating this gives:

\[
A(7) \approx 448.74
\]

Rounding to the nearest tenth, we find:

\[
A(7) \approx 448.7
\]

Thus, after 7 years, approximately **448.7 grams** of Radium-226 will remain.