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

Question

. How many grams of Radium-226 will remain after seven years? Round your answer to the nearest tenth.

Answer 1

To find the amount of Radium-226 remaining after seven years, we can use the given decay formula:

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

We need to evaluate \( A(7) \):

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

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

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

Now substitute this value into the equation:

\[ A(7) = 450e^{-0.0028} \]

Next, we calculate \( e^{-0.0028} \):

Using a calculator or mathematical software:

\[ e^{-0.0028} \approx 0.9972 \]

Now, substitute back to find \( A(7) \):

\[ A(7) = 450 \times 0.9972 \approx 448.74 \]

Finally, rounding this to the nearest tenth gives:

\[ \boxed{448.7} \text{ grams} \]

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