Question

If 340 grams of a substance are present initially and 50 years later only 170 grams remain, how much of the substance will be present after 120 years?Round to the nearest tenth of a graim.grams

Answer 1

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:

`\text{ A = S\lparen}(1)/(2)\text{\rparen}^{(t)/(h)}`

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:

`\begin{gathered} A\text{ = 340}*((1)/(2))^{(120)/(50)} \\ \\ A\text{ = 17\lparen}(1)/(2)\text{\rparen}^(2.4) \\ \\ A\text{ = 17}*(0.5)^(2.4) \\ \\ A\text{ = 17}*0.1894 \\ \\ A\text{ = 3.22 gram} \end{gathered}`

Final Answer -

The substance that will remain after 120 years = 3.22 gram