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)
o 548.8 grams
o 344.8 grams
o 468.9 grams
o 448.7 grams

Explanation:

Step1: Substitute $t = 7$ into formula

$A(7)=450e^{- 0.0004\times7}$

Step2: Calculate exponent value

First, calculate $-0.0004\times7=-0.0028$. Then $A(7)=450e^{-0.0028}$.
Since $e^{-0.0028}\approx0.9972$, then $A(7)=450\times0.9972$.

Step3: Calculate final result

$450\times0.9972 = 448.74\approx448.7$

Answer:

448.7 grams