Question

I wasn't aware that this was even included in a calculus course but anyhow,

Find the exponential function f(x) = Ca^x that passes through the ordered pairs (-1,3), and (1,4/3).

Answer 1

I've tried solving with subsitution and come up with either f(x)=(1/3)^x or f(x)=4(1)^x. Both only work to find one point or the other.

Answer 2

I mean f(x) = 4(1/3)^x.

Answer 3

It's as easy as solving the system:

C/a=3
C*a=4/3

Answer 4

I don't understand what I'm doing wrong. The equation just doesn't check.
Here is my work:
3=c/a or a=c/3
ca=4/3 or c=(4/3)-a
Substituting, c=(4/3)-(c/3)
c=(4-c)/3
3c=4-c
4c=4
c=1

Back-substituting, a=c/3 =1/3
Therefore, f(x)=Ca^x=1(1/3)^x

Answer 5

Well first it's not ''or'' it's ''and'' because it's a system. Also you made a little mistake in the second line ''c = 4/3 - a''

Answer 6

I really don't see the difference between using or and and alternatively here because either one you pick is that same, and thanks for catching that mistake.

Answer 7

Alright, cool, I ended up with f(x)=2(2/3)^x. It checks out alright.

Answer 8

Great !

''Or'' means one of the 2 equations can be wrong. which is not true because we got both of them from the ordered pair given above.

Answer 9

Also, do you know how we got that system ?

Answer 10

Yeah, I guess I should know that since the degree I'm going to college for is computer science.

Answer 11

Yes, you just insert the x and y values for each point and get two separate equations

Answer 12

Computer science :) That's cool

Answer 13

Well, thanks man, I probably would have sat here another hour if you didn't come along. Have a good one.

Answer 14

You're welcome !