A friend of mine asked for my help with her homework but it's been so long since last time I solved problems like that I'm not sure if what I did was right.

in before you ask me to post what I've done, that won't be possible as I can't take a picture of it right now and don't have the right software to write equations so it would look a mess.

Here are the questions:

 

It is estimated that at the current rate of consumption, r gallons per year, the oil supply of the earth will last 200 years. However, the rate of consumption, R(t) is increasing at the rate of 5% per year; that is dR/dt=.05R

a) In terms of r, how many gallons of oil are currently available?


b) Use the given differential equation to find R(t)


c) If no additional oil is discovered, how long, to the nearest year, will the current oil supply actually last?

Edited April 24, 201114 yr by Lessa

How did you start this, Lessa? any ideas? do you know what equations to use here, or where you start to get your rates?

a) It's kinda obvious. if the consumption rate is r and it would last for 200 years the total amount of oil has to be -200r.

 

b) dR/dt=0.05R -> R(t) = e^0.05t (not sure if that one is right).

 

c) 200 = e^0.05t -> t = 106 (also not sure about that one).

 

I actually don't have a clue on how to explain what I did but if I'm on the right way you can probably figure it out.

That looks about right.

 

dR/R = .05 dt

 

ln R = .05 t

 

R(t) = exp(.05t)

 

So ln(200)/.05 = t

Edited April 24, 201114 yr by Fuzzwood