8. After *x *weeks the number of persons using a new drug was _{}. At what percentage rate was the use of the drug changing after four weeks?

**Solution: **Let’s compute

_{}

We can take two approaches: by derivatives (approximation) or exactly:

After four weeks the derivative is computed as

_{}

which means that approximately 208 new people a week use the drug after four weeks. We also know that

_{}

the percentage rate the use of the drug is changing after four weeks is 10.4% (approximation using derivatives).

We can compute the percentage exactly as:

_{}

**(b) By how much did the number of persons using this drug actually change during the fourth week?**

**Solution: **We can find the exact change computing

_{}