Derivative of P(x) = 0.2 -0.125e^(0.005x) for X=1

[masterchiefo]

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

does that simply mean that the population is going down over time?

 

[Noctisdark]

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 ?]

 

[Mark44]

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

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.

does that simply mean that the population is going down over time?

 

[masterchiefo]

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.

Thats because my calculator calculated e^0.005*x = 1.00501^x

 

[masterchiefo]

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 ?]

Yeah I wrote down the derevative of P in terms of x and I believe that since its negative the population is decreasing ?

 

[Noctisdark]

Yepp, great work .

 

[masterchiefo]

Yepp, great work .

thanks awesome.

This forums makes me like University even more :) I love school & studying :)

 

[Mark44]

Thats because my calculator calculated e^0.005*x = 1.00501^x

Operator error

To make that calculation, you need parentheses, as in e^(.005*x).

 

[Mark44]

Yepp, great work .

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.

 

[masterchiefo]

Operator error

To make that calculation, you need parentheses, as in e^(.005*x).

oh ok thank you very much :)