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

Question

−0.0004t
.
How many grams of Radium-226 will remain after seven years? Round your answer to the nearest tenth.
□ grams

Answer 1

To find the amount of Radium-226 remaining after seven years, we can substitute \( t = 7 \) into the equation:

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

Substituting the value of \( t \):

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

Calculating the exponent:

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

Now substituting this value back into the equation:

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

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

Using a calculator, \( e^{-0.0028} \approx 0.9972 \).

Now multiply by 450:

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

Finally, rounding to the nearest tenth:

\[ A(7) \approx 448.7 \]

Thus, the amount of Radium-226 remaining after seven years is approximately 448.7 grams.