Hello, TC!

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 .

Italreadysatisfies the problem . . .the base does not matter.

So pickanytwo positive bases (other than 1).

I'd offer: .

. . but you can use your imagination . . .

Examples

. .

. .