Can you please help me do this question? I'm really stuck?
n=400/(1 + 9e^((-1/9) t)
Show that the above equation can be written in the form
t = 9ln ((9n)/(400 - n))
I know it's difficult to read when its typed out, but could you please offer some help? Would you mind showing me the method?
Thanks
D
n=400/(1 + 9e^((-1/9) t)
Show that the above equation can be written in the form
t = 9ln ((9n)/(400 - n))
I know it's difficult to read when its typed out, but could you please offer some help? Would you mind showing me the method?
Thanks
D
-
400 = (1 + 9e^((-1/9) t) n
400 = n + 9n e^((-1/9) t)
9n e^((-1/9) t) = 400 - n
e^((-1/9) t) = (400 - n) / (9n)
e^((1/9) t) = (9n) / (400 - n)
(1/9) t = ln [ (9n) / (400 - n) ]
t = 9 ln [ (9n) / (400 - n) ]
400 = n + 9n e^((-1/9) t)
9n e^((-1/9) t) = 400 - n
e^((-1/9) t) = (400 - n) / (9n)
e^((1/9) t) = (9n) / (400 - n)
(1/9) t = ln [ (9n) / (400 - n) ]
t = 9 ln [ (9n) / (400 - n) ]