Question

You have 900-grams of an an unknown radioactive substance that has been determined to decay according to

D(t)=900e−0.002415⋅t

where t is in years. How long before half of the initial amount has decayed?

It will take ____ years for half of the initial amount to decay. (Round to 1 decimal place)

Answer 1

The initial amount is 900, half of this is 450. So set the equation equal to 450 and solve for t.

$450=900e^{-0.002415t} \\ \\ \frac{450}{900} = e^{-0.002415t}$

Natural logarithm (ln) is base "e" Euler's number

$ln( \frac{450}{900} = ln( e^{-0.002415t} ) \\ \\ln( \frac{450}{900} ) = -0.002415t \\ \\ \frac{ln( \frac{450}{900}) }{-0.002415} = t \\ \\ t = 287.0 yrs$