The number of trees in a forest is decreasing at a rate of 5% per year. The forest had 24,000 trees 15 years ago. Write an exponential decay function to model situation, Then find out how many trees there are now.

Question

parthkohli · Answer

$\Large \color{MidnightBlue}{\Rightarrow 24000(1 - {5 \over 100})^n }$

This is another kind of compounding continuity. Hehe.

parthkohli · Answer

Hi @dumbcow :)

anonymous · Answer

$$T(t)=24000e^{.05t}$$Standard exponential decay function.  Substitute t=15 to get then number of trees now.  A thumbnail estimate might indicate about 12000 (without a calculator).

dumbcow · Answer

general decay function
$$P_t = P_0 (1-r)^{t}$$
r = .05

@ParthKohli Hi back

anonymous · Answer

I don't think this kind of phenomenon is usually modeled with the periodically compounded interest formula.  Exponential decay function is the usual model.  The answers won't be too different for this short of a time.

anonymous · Answer

OOPS!!  I left the negative sign out of the formula!!  Epic fail.

anonymous · Answer

$$T(t)=24000e^{-.05t}$$
Standard exponential decay function.  Substitute t=15 to get then number of trees now.  A thumbnail estimate might indicate about 12000 (without a calculator).

anonymous · Answer

That one is better.  Just like in the textbook....

anonymous · Answer

OK, the answer is very close anyway.  My formula gives about 11300 trees.  I don't think there is any justification for using the financial payment model as you did to model a natural process like the decay of a forest.

dumbcow · Answer

wow i think i may have been mistaken here...it does say exponential decay model :|
i apologize... i have been doing too many geometric series problems, of course natural process involve continuous rates