Question

Write an exponential function whose graph passes (0,1) and (6,64)?

Answer 1

you need to find:

\[e^{f(x)} \] such that\[e^{f(0)} = 1\]
and
\[e^{f(6)} = 64\]

You can pick any function that satisfies those. Simplest function to take would be a linear function, and in this case we can:

f(x) = ax + b and we want to find a and b that satisfy these; and we don't even have to use b, but we can. (they said pick one function. i can come up with an infinite amount)

6a = 64 --> a = 32/3

so a function that works is:

\[e^{\frac{ 32x }{ 3 }}\]

Answer 2

Thank U

Answer 3

but I dont understand why u say linear

Answer 4

because the question ask for exponential function

Answer 5

I need clarification as a blueprint to do the many others that I have in this regard... HELP

Answer 6

by linear i meant the f(x). in e^(f(x))

for f(x) I could have picked a non-linear function (2nd order or higher), but I would have just complicated things.

I could have found a function ax^2 + bx that would have satisfied the two conditions.

But then again that's complicating things.

You can always solve this using a linear function (a first order polynomial), which looks like ax + b (where b can = 0) exists in the form:

\[e^{ax + b} \]

or simply and often:

\[e^{ax}\]

I hope i cleaned up my mess a bit :P

Answer 7

wow my answer is wrong above. very wrong

Answer 8

OK

Answer 9

e^(ax)=64=e^(6a)


so to solve for a the real actual way (idk what i was thinking)

ln(64) = 6a

a = ln64/6

function is then:

\[f(x) = e^{\frac{ (\ln64)x} {6 }}\]

Answer 10

OK thank U