Question

Supose that the half-life of a cesium is 30 years. If there were initially 1000g of the substance,

Answer 1

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:

$N(t)=ab^t$

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:

$N(t) =1000(\frac{1}{2} )^{\frac{1}{30} t}\\\\N(t) =1000(\frac{1}{2} )^{\frac{t}{30}$

b) After 200 years (t = 200), the amount of Cesium remaining is:

$N(200)=1000(\frac{1}{2} )^\frac{200}{30} \\\\N(200) = 9.84g$

Hence after 200 years, 9.84 grams of Cesium would remain

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