which of the following is the equation of the exponential function y=Ce^kx that passes through (0,1) and (1,1/e)
a)y=e^kx
b)y=ce^x
c)y=e^x
d)y=e^-x
e)none

Question

which of the following is the equation of the exponential function y=Ce^kx that passes through (0,1) and (1,1/e) 
a)y=e^kx
b)y=ce^x
c)y=e^x
d)y=e^-x
e)none

anonymous · Answer

why u dont just replace (0,1) and (1,1/e)  into the functions and see what match¡?

anonymous · Answer

i tried it already but i did not make sense

anonymous · Answer

really? the (d) dont match?

agent0smith · Answer

plug in (0, 1)
$$\Large 1=Ce^{k \times 0}$$giving 
$$\Large 1 = C$$

agent0smith · Answer

Now plug in (1, 1/e)
$$\Large \frac{ 1 }{ e }=e^{k \times 1}$$$$\Large \frac{ 1 }{ e }=e^{k}$$
either take logs of both sides, or do this$$\Large e^{-1} = e^k$$

anonymous · Answer

so then i  put them together

agent0smith · Answer

Yes, now you have both C and k.

anonymous · Answer

for the last problem you were doing was the answer k=-1

agent0smith · Answer

Yep :)

anonymous · Answer

oh ok so i first plug in the values then i solve for the values of c and k i think i get it now

agent0smith · Answer

Which equation did you get?

anonymous · Answer

i got d y=e^-x

agent0smith · Answer

:)