Question

The weight (W kg) of a decaying radio active substance after n years is given by W= Wo(1/2)^n/100, where Wo kg is the initial weight of the substance. 1. Find the number of years for the radioactive substance to decay to half of its initial weight.Atleast how many years will it take for the radioactive substance to lose to 10% of its initial weight?

Answer 1

Step-by-step explanation

The weight (W kg) of a decaying radio active substance after n years is given by:

`\begin{gathered} W=W_0((1)/(2))^{(n)/(100)} \\ \text{Where }W_0kg\text{ is the initial weight of the substance.} \end{gathered}`

To find the number of years for the radioactive substance to decay to half of its initial weight, it implies the weight of the substance at that number of years will be:

`W=(1)/(2)W_0`

Therefore,

`\begin{gathered} (1)/(2)W_0=W_0_{}((1)/(2))^{(n)/(100)} \\ \text{Divide both sides by W}_0 \\ ((1)/(2))^1=_{}((1)/(2))^{(n)/(100)} \\ Equate\text{ the exponents} \\ 1=(n)/(100) \\ n=1*100 \\ n=100\text{ years} \end{gathered}`