Question

how do you differentiate N=100t(e^-1/12)+500 and make equal to zero?

Answer 1

is it e^(-t/12) or just e^(-1/12 ?

Answer 2

e^1/12

Answer 3

dN/dt is simply 100e^(-1/12). a constant function. it is never equal to zero. always equal to the constant

Answer 4

but i need to equate to zero to find the max value

Answer 5

if the initial N occus January 1986, how do i find when the max N will occur?

Answer 6

you may have miswrote the function.

Answer 7

Population growth is e^(at)

Answer 8

Po*e^(rate*t)

Answer 9

yes, the function is N=100te^-1/12+500

Answer 10

e is to the power of -1/12, isn't that right? how do i differentiate it and find the max?

Answer 11

oh, wait, so sorry, it is -t/12, it was written wrong in my notes.

Answer 12

hehe. in that case you must use product rule.

(f(x)*g(x))' = f'(x)g(x) + f(x)g'(x)

Answer 13

f(x) = t and g(x) = e^(-t/12). the rest are all constants

Answer 14

so its 100 ( 1*e^(-t/12) + t*(-1/12)*e^(-1/12)

Answer 15

= 100 ( 1 - t/12) (e^(-t/12))

this function is only = 0 when t = 12 (since e^x is never = 0)

Answer 16

i don't understand how you got from the first line of working to (1-t/12), i understand the second bracket

Answer 17

i don't understand what you don't understand :P lol.

i factored out e^(-t/12)

Answer 18

oh, okay.

Answer 19

i don't understand how you got t=12

Answer 20

if you make the brackets equal 0, doesn't the first equal zero, but the second -1?

Answer 21

1-t/12=0 so t=-1?????

Answer 22

how do you make the brackets equal zero
( 1 - t/12) -->doesn't this one equal -1 if you divide by 12

(e^(-t/12))-->and this one 0

i'm so confused?

Answer 23

oops i meant times by 12

Answer 24

(1 - t/12) = 0 --> 1 = t/12 ---> t = 12

Answer 25

e^(-t/12) can never = 0 since its the exponential function.

Answer 26

doesn't e^0 equal 1 though, so wouldn't making t=0 make e^0/12-->1

Answer 27

it would. but nobody wants to do that. were looking for t values which make the derivative of the function = 0

Answer 28

okay, i don't really get the last bit, but i get the main gist