Integrate exponential question (1 Viewer)

[enigma_1]

A curve has gradient (3^−x)(log 3) and an horizontal asymptote of y = 2. Find the
equation of the curve and its y-intercept.

I got the primitive, but now how do I find "C"?

 

[youngsky]

Assuming you got the primitive y = -e^[-xln(3)] + C, to find C; use the information given that a horizontal asymptote is y = 2

That is, an asymptote simply means a value for which the curve does not exist in - this case is y = 2.

So, let y = 2 into your primitive:

2 = -e^[-xln(3)] + C

What we can see is that there's 2 things on RHS, an exponential and a constant. We know that an exponential's asymptote (given no constants involved) is y = 0. So to make y = 0 (the LHS), let C = 2.

2 = -e^[-xln(3)] + 2
0 = -e^[-xln(3)] + 0
0 = e^[-xln(3)]

Looks like it all works out if C = 2. So yeah, pretty sure it's C = 2