No.masterchiefo said:Homework Statement
Derivative of P(x) = 0.2 -0.125e^(0.005x) for X=1
P(x) is the population in Millions and X is the year where 0 = 2000
I have to explain the answer I am getting at the end.
Homework Equations
The Attempt at a Solution
d/dx (0.2 -0.125e^(0.005x))
I find -0.000625*(1,00501)^x // did this with my calculator
-0.000625*(1,00501)^1 = -0.000628
masterchiefo said:does that simply mean that the population is going down over time?
Thats because my calculator calculated e^0.005*x = 1.00501^xMark44 said:No.
I don't know what you entered into your calculator, but it came out wrong. The derivative should involve e raised to the power kx.
I would advise putting your calculator away and doing this by hand. You're more likely to get the right answer.
Yeah I wrote down the derevative of P in terms of x and I believe that since its negative the population is decreasing ?Noctisdark said:Welcome to PF,
Great work, just want to point at something, P(x) = 0.2 -0.125*e^(0.005)
It has a something constant - some exponontial, so it will be decreasing so fast over the years,
Hope I've helped,
[Edit: To answer, you have to write down the derevative of P in terms of x, and what should it's sign be to be decreasing ?]
thanks awesome.Noctisdark said:Yepp, great work .
Operator errormasterchiefo said:Thats because my calculator calculated e^0.005*x = 1.00501^x
Please pay closer attention before making comments about the correctness of a poster's work. The OP made a gross error in his first post, which you apparently didn't notice.Noctisdark said:Yepp, great work .
oh ok thank you very much :)Mark44 said:Operator error
To make that calculation, you need parentheses, as in e^(.005*x).
The derivative of P(x) at x=1 is 0.000625.
The derivative of P(x) can be calculated using the power rule and the chain rule. In this case, the derivative is 0.005e^(0.005x).
The derivative represents the rate of change of P(x) at a specific point (x=1). It can also be interpreted as the slope of the tangent line to the curve at that point.
The overall trend of P(x) is a decreasing exponential function. As x increases, the value of P(x) decreases at a decreasing rate.
The derivative of P(x) can be used in various fields such as physics, economics, and engineering to analyze rates of change and make predictions. For example, in economics, the derivative can be used to determine the marginal cost of production at a specific level of output.