After 200 years, 9.84 grams of Cesium would remain.
Let N represent the amount of substance after t years
The half-life of a cesium is 30 years., hence, this can be represented by exponential function:
[tex]N(t)=ab^t[/tex]
where a is the initial value and b is the multiplier.
There were initially 1000g of the substance
a) The exponential model for this situation is:
[tex]N(t) =1000(\frac{1}{2} )^{\frac{1}{30} t}\\\\N(t) =1000(\frac{1}{2} )^{\frac{t}{30}[/tex]
b) After 200 years (t = 200), the amount of Cesium remaining is:
[tex]N(200)=1000(\frac{1}{2} )^\frac{200}{30} \\\\N(200) = 9.84g[/tex]
Hence after 200 years, 9.84 grams of Cesium would remain
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