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Oil consumption is increasing at a rate of 1.9% per year. What is its doubling time? I'm not sure if this is linear increase or exponential. if its linear
, no , this website says its exponential http://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.112025.html
, if its linear then y = Ao ( 1 + .06*t ) if its exponential then y = Ao ( 1 + .06)^t
i think its exponential 2 = 1 ( 1 + 0.06)^t now calculate t
Oh, wait. That's right. I apologize. I graphed it wrong.
how will i know if its exponential or not?
here is another example http://www.physics.uoguelph.ca/tutorials/exp/intro.html
why isnt the following example linear ? "For example, let's look at a population of wee beasties which increases by 10% per year. If there were 100 wee beasties now, there would be an increase of 10 wee beasties after a year. "
see in question it increases 1.9% per year first year let consumption = x next year = 1.9*x/100 later year = 1.9(1.9*x/100)/100 if you plot its graph you get exponential curve try it
in your second example population first year = 100 population second year = 110 population third year = 121 it also not linear
it should be next year consumption = last year consumption* ( 1 + 1.9/100)
so we have x1 = x x2 = x1 (1.019) x3 = x2 (1.019) = [x1 (1.019) (1.019) ]
better start with zero, x0 = x x1 = x0 (1.019) x2 = x1 (1.019) = [x0 (1.019) ] (1.019) = x0 (1.019) ^2
calculate x1,x2 ,x3 and try to find x2 - x1 = x3 -x2 if its write then only its linear
so did you agree with my math?
right, clearly x2-x1 != x3 - x2
yes i agree so what you think its linear or exponential
i think its a little ambiguous however
, you could also have y = x0 ( 1 + .019 * t ) , no ?
ok how would you word it so that it is linear?
let if increase every year is same then its linear for example if population of city inc by 20 people every year then we can say that its linear
ok , so we wouldnt use percentage for a linear increase
if there is a percentage growth , like population percentage growth , grows at a constant percentage, it is exponential growth
ok now doubling time makes sense
doubling time is the time it takes for the initial amount to grow 100% , leaving you with double
yes did you get your answer?
yes, the math i didnt have trouble with. just the understanding
i have a much harder problem, differential equation
its a logistic growth problem
ok then now you can close the qustion after giving me medal...............lol
you stuck it out , good work