Great Problem. Interestign catch though; Try It! I'll show you what the catch is.

**1) **In New York City, the number of arrests for possession of marijuana has increased dramatically as indicated in the table below.

**a) **Let f(t) represent the number of arrests (in thousands) for possession of marijuana at years since 1990. Find an exponential formula for f(t)?

**1992**

**1.0**

**1993**

**2.4**

**1994**

**3.9**

**1995**

**7.0**

**1996**

**11.0**

**1997**

**19.8**

**b) **What is the coefficient (a) of the function f(t)=a(b)^t? What does it mean in terms of the number of arrests?

**c) **What is the base b of function f(t)= a(b)^t ? What does it mean in terms of the number of arrests?

**d) **According to your model f(t) when will there be 1 million arrests (you must determine this by solving an equation by hand – and show your work)? In your opinion, is this possible? Explain.