Question

Can someone help me please

The half-life of strontium-90 is 28 years. How long will it take a 40 mg sample to decay to a mass of 10 mg?
Your answer is ------------ years.

Answer 1

`\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( (1)/(2) \right)^{(t)/(h)}\qquad \begin{cases} A=\textit{current amount} &\dotfill 10\\ P=\textit{initial amount}\dotfill &40\\ t=\textit{years}\\ h=\textit{half-life}\dotfill &28 \end{cases} \\\\\\ 10 = 40\left( (1)/(2) \right)^{(t)/(28)} \implies \cfrac{10}{40}=\left( (1)/(2) \right)^{(t)/(28)}\implies \cfrac{1}{4}=\left( (1)/(2) \right)^{(t)/(28)}`

`\log\left( \cfrac{1}{4} \right)=\log\left[ \left( (1)/(2) \right)^{(t)/(28)} \right]\implies \log\left( \cfrac{1}{4} \right)=t\log\left[ \left( (1)/(2) \right)^{(1)/(28)} \right] \\\\\\ \cfrac{ ~~ \log\left( (1)/(4) \right) ~~ }{\log\left[ \left( (1)/(2) \right)^{(1)/(28)} \right]}=t\implies 56 = t`