Question 982411
There is some room for confusion, just as there is room for multiple answers.
A popular exponential function is {{{y=e^x}}} {{{graph(300,300,-3,3,-1,9,e^x)}}} ,
but there is nothing sacred to that number {{{e}}} until you get to calculus.
The function {{{y=2^x}}} {{{graph(300,300,-3,3,-1,9,2^x)}}} is also an exponential function.
A power of any base is an exponential function, but if you try a base such as {{{0.9<1}}} , you get a reversed graph: {{{drawing(300,300,-20,20,-0.2,4.5,locate(4,1,red(y=0.9^x)),graph(300,300,-20,20,-0.2,4.5,0.9^x))}}} .
We can use any base greater than {{{1}}} and we would get an exponential function with the same basic qualities:
1) it has a y- intercept of {{{1}}} , so it passes through the point (0,1),
2) its horizontal asymptote is y=0, and
3) the slope of the line passing between any two points on the graph is positive.
So far, quality number 3) meets the requisites of the problem.
To nail 1) and 2) we can stretch the graph vertically, and translate it down.
The functions above had an (invisible) {{{1}}} as a coefficient multiplying the power,
and the difference between the y-value of the asymptote and the y-intercept was {{{1}}} .
If we multiply times {{{31-(-73)=31+73=104}}} , as in {{{y=104e^x}}} ,
the difference between the y-value of the asymptote and the y-intercept will be {{{104}}} ,
which happens to be the difference between "a y-intercept of 31 and a horizontal asymptote of -73".
If next we move the graph down by {{{73}}} units by adding a {{{-73}}} ,
we get {{{y=104e^x-73}}} : {{{drawing(300,300,-5,1,-93,217,locate(-2.3,-73,green(y=-73)),graph(300,300,-5,1,-93,217,104e^x-73,-73))}}} .