At $10$:$00$ a.m. a radioactive material weighed $2$ grams, but at $6$:$00$ p.m. it only weighed $0.45$ grams.

1. Write an equation to model this situation.

   Hint (a):

   You will need to write an equation of the form $y = ab^x$. Substitute the given information
   into the general equation and solve for the desired values.

2. What are the approximate hourly multiplier and the hourly percent of decrease?

   Answer (b):

   $\approx0.83$ or a $17\%$ decrease

3. What was the weight of the material at $8$ a.m.?