Answer:
The mass of the substance that will remain after 5 years is 3.15 g
Step-by-step explanation:
Given;
initial mass of the radioactive substance, a = 10 g
remaining mass after 3 years, y = 5g
Generating a half-life equation;
[tex]y = ab^x\\\\5 = 10b^3\\\\\frac{5}{10} = b^3\\\\0.5 = b^3\\\\log(0.5) = log(b^3)\\\\3log(b) = log(0.5)\\\\log(b) = \frac{1}{3} log(0.5)\\\\log(b) = log(0.5)^{\frac{1}{3}} \\\\b = 0.5^{\frac{1}{3}} \\\\b = 0.7937\\\\y = 10(0.7937)^x\\[/tex]
After 5 years, the mass of the substance that will be present is given by;
y = 10(0.7937)⁵
y = 3.15 g
Therefore, the mass of the substance that will remain after 5 years is 3.15 g
