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

1. Apr 9, 2015

### masterchiefo

1. The problem statement, all variables and given/known data
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.
2. Relevant equations

3. 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?

2. Apr 9, 2015

### 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 ?]

3. Apr 9, 2015

### Staff: Mentor

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.

4. Apr 9, 2015

### masterchiefo

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

5. Apr 9, 2015

### masterchiefo

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

6. Apr 9, 2015

### Noctisdark

Yepp, great work .

7. Apr 9, 2015

### masterchiefo

thanks awesome.

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

8. Apr 9, 2015

### Staff: Mentor

Operator error

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

9. Apr 9, 2015

### Staff: Mentor

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.

10. Apr 9, 2015

### masterchiefo

oh ok thank you very much :)