Because of an economic slump, a company finds that its annual profits have dropped from 600 thousand dollars in 2006 to 400 thousand dollars in 2009. If profit follows an exponential decline, what's the expected profit in 2010?
Hint: Your calculations will be easier if you let t=0 correspond to the year 2006.

Can some explain how to solve these kinds of problems?

Question

Because of an economic slump, a company finds that its annual profits have dropped from 600 thousand dollars in 2006 to 400 thousand dollars in 2009. If profit follows an exponential decline, what's the expected profit in 2010? 
Hint: Your calculations will be easier if you let t=0 correspond to the year 2006.

Can some explain how to solve these kinds of problems?

dumbcow · Answer

start with  a general exponential decline function:
$$f(t) = A e^{-kt}$$
A is intial value
you are given 2 points (t, f(t))
plug those in and you end up with system of 2 equations 
solve for A and k

dumbcow · Answer

for this problem....2006 is starting point (t=0) so 2009 is t=3 and 2010 is t=4
let profits be in terms of thousands
(0,600)
(3,400)
$$600 =A$$
$$400 = A e^{-3k}$$

anonymous · Answer

Thanks:) I was able to solve it awhile ago.

dumbcow · Answer

oh ok :)