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 answers to the nearest tenth.(1 point)

Answer 1

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

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

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

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

Now, substitute this back into the equation:

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

Next, we need to calculate \( e^{-0.0028} \). Using a calculator:

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

Now, multiply this by 450:

\[ A(7) \approx 450 \times 0.9972 \approx 448.736 \]

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.