Find an exponential function with given condition How can I have an example of an exponential function defined in the X range 1 - infinity, with values starting at 40 and converging to 1?

Since this cannot be a pure exponential function, let's try some others.  
$1+39k^{x-1}$ is one possibility for any $0 \lt k \lt 1$ and and produces functions $1$ more than an exponential function.
$40 x^{1/x^k}$ for any $k \gt 0$ may have the sort of shape you are looking for, but I think it is not an exponential function. 
