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

Answer 1

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

Answer 2

i tried it already but i did not make sense

Answer 3

really? the (d) dont match?

Answer 4

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

Answer 5

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\[\Large e^{-1} = e^k\]

Answer 6

so then i put them together

Answer 7

Yes, now you have both C and k.

Answer 8

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

Answer 9

Yep :)

Answer 10

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

Answer 11

Which equation did you get?

Answer 12

i got d y=e^-x

Answer 13

:)