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

• Jul 14th 2008, 08:26 AM
racersteve47
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.

Year
Arrests (thousands)
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.
• Jul 14th 2008, 08:27 AM
racersteve47
typing typo
Also! that should have turned up as a table the year (i.e.) 1992 is corresponding to the number below it (i.e) 1.0
• Jul 14th 2008, 10:41 AM
racersteve47
an attempt?
So has no one attempted?
• Jul 14th 2008, 01:47 PM
topsquark
Quote:

Originally Posted by racersteve47
So has no one attempted?

Give it a day or so. Personally, I'm simply too lazy to do an exponential best fit. :)

-Dan
• Jul 14th 2008, 02:27 PM
galactus
I ran it through Excel and get:

EXPONENTIAL:

$y=.3725e^{0.5737x}$

POWER:

$y=.1868x^{2.3027}$