This is trickier than you think . . .
Write two different exponential equations with different bases
which have a y-intercept of 5 and an asymptote at y=3.
An exponential function can have a coefficient in front: .
This equation has a horizontal asymptote at (the x-axis).
To have an asymptote at , we must "raise" the function 3 units.
. . So we have: .
To have a y-intercept of 5, we want: . and
. . Substitute: .
Hence, the function is: .
This equation has a graph with a y-intercept of 5 and an asymptote at .
It already satisfies the problem . . . the base does not matter.
So pick any two positive bases (other than 1).
I'd offer: .
. . but you can use your imagination . . .