Respuesta :
Given -
Substance present initially = 340 grams
Substance present 50 years later = 170 grams
To Find -
How much of the substance will be present after 120 years =?
Step-by-Step Explanation -
Since the substance was reduced to half of what it is initially in 50 years.
So,
The half-life time of the substance = 50 Years.
It means that every 50 years, the substance will reduce to half of its quantity.
And, we know the formula:
[tex]\text{ A = S\lparen}\frac{1}{2}\text{\rparen}^{\frac{t}{h}}[/tex]Where,
A = the remaining amount of Substance =?
S = the amount of Substance you start with = 340grams
t = the amount of time in years = 120 years
h = the half-life time = 50 years
Simply putting the values, we get:
[tex]\begin{gathered} A\text{ = 340}\times(\frac{1}{2})^{\frac{120}{50}} \\ \\ A\text{ = 17\lparen}\frac{1}{2}\text{\rparen}^{2.4} \\ \\ A\text{ = 17}\times(0.5)^{2.4} \\ \\ A\text{ = 17}\times0.1894 \\ \\ A\text{ = 3.22 gram} \end{gathered}[/tex]Final Answer -
The substance that will remain after 120 years = 3.22 gram
