P - PoAt OR P = Poe KT

[llewis1]

Problem: During 1980's, Country had highest deforestation rate @ 2.9%. Assuming rate continues what % of land in Country covered by forests in 1980 will be forested in 2015?

Just started Applied Calculus (course taught w/ TI 83) a few weeks ago; and math is not my strong suit.

First; looking at the problem how on earth do you decide which formula to use>
I'm thinking the P = Po e ^kt (because the rate "continue"); but for all I know I should use the P = Po A ^t.

If A = 1 +r; then A = 1 + .029; or A = 1.029.

So I have an amt to insert into A (or k):

If I go with the: P = Po A ^t; then
P = Po (1.029)^t [Note: If 1980 can be considered P(0); then I'm thinking that 2015 would be P(35).

P(35) = Po (1.029)^35
[take the 35 root of both sides]
P = Po (1.029)
.....now what?

If I go with the P = Po e kt
P = Po e (1.209^t)
P(35) = Po e (1.209^35)
[take the 35 root of both sides}
P = Po e (1.209)
....now what?

I feel pretty lost guys..any help would be greatly appreciated.

 

[wjm11]

Problem: During 1980's, Country had highest deforestation rate @ 2.9%. Assuming rate continues what % of land in Country covered by forests in 1980 will be forested in 2015?

Your problem statement is unclear. Are you assuming 2.9% forest loss each year? If so, you have 1-.029 = .971 remaining from the prior year. So

P = Po(.971)^n gives you the remaining forest for each year, n.
For 2015, n = 2015 – 1980 = 35

If your problem statement is something else, please state it EXACTLY as it appears in your book.

 

[soroban]

Hello, llewis1!

During 1980's, Country had highest deforestation rate @ 2.9%.
Assuming rate continues, what % of land in Country will be forested in 2015?

I will assume that the problem starts in 1980. .Otherwise, we can't solve it.

And we can use: \(\displaystyle \\;=\;P_oe^{kt}\)


We are told that in 1980, the rate was: \(\displaystyle k\,=\,-0.029\) which is constant.
. . So we have: \(\displaystyle \\:=\_oe^{-0.029t}\)


In 2015 \(\displaystyle (t\,=\,35)\), we have: \(\displaystyle \,P\:=\_oe^{(-.0.29)(35)}\)

Then: \(\displaystyle \:\frac{P}{P_o}\;=\;e^{-1.015} \;=\;0.36240243 \;\approx\;36\%\)


Therefore, in 2015, only 36% of the forested lands will remain.

 

[llewis1]

Exact Problem: During the 1980, Costa Rica had the highest deforestation rate in the world, at 2.9%/year (This is the rate at which land covered by forests is shrinking). Assuming the rate continues, what percent of the land in Costa Rica covered by forests in 1980 will be forested in 2015?


If P = Po A ^t
P = Po (.971)^35 two questions:

1. Why did you use 1 - A? or 1 - .029? Prof gave us A = 1 + R ( and therefor, I understand that R = A-1). Was it just a process of elimination thing based on the problem, you knew that you were looking for the remaining percent?
2. I have a brain freeze at this point. For some reason, I cannot solve/factor the remainder of the problem.

Thanks SO MUCH for the help!

 

[llewis1]

Good morning, Soroban -

Thanks for the reply/explanation. It follows the lines of where my "very elementary" train of thought figured I should be heading.

But for other similar problems, what's the "Reader's Digest" version on how to decide which formula to use (the Po A ^T or the Po e ^kt)?

 

[wjm11]

1. Why did you use 1 - A? or 1 - .029? Prof gave us A = 1 + R ( and therefor, I understand that R = A-1). Was it just a process of elimination thing based on the problem, you knew that you were looking for the remaining percent?

Not by a "process of elimination". The term deforestation implies a "decrease." The rate of deforestation , or decrease, is 2.9%. Since we are not calculating the amount by which the forest is reduced, but rather wish to know the amount of forest remaining, we must use 1-(rate of decrease), the "remaining percent." Hope that helps.