The time rate of decay of Cesium - 37 with t years is proportional to the mass, m. 50% of Cesium - 37 remains after 30 years.

1. (a)Find by integration, an expression for the mass, m, that remains after t years.
2. (b)Suppose we have a starting amount of 200 mg. How much of the sample remains after 100 years? Give both the exact answer and evaluate with calculator to 2 decimal places.