Question

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Answer 1

y = 2*3^x is an exponential function whose y-intercept is at y = 2 and asymptote y = 0.
So if we translate this 3 units up, the y-intercept will be y=5 and horizontal asymptote at y=3. So the example y = 2*3^x + 3 is an example of your question. another would be
y = 2*e^x + 3.

Answer 2

the e is just a constant (very well known in physics and math). It has a value approximately equal to 2.71828.... It is an irrational number like pi.

in fact, you can replace that with any positive number to get your answers... In my examples, I used 3 and e as the base for the exponential function.

Answer 3

try graphing it. you'll see that the conditions you required are met.

Answer 4

just let x=0 and solve for y in your equation...