Software developer salaries grow with experience. Suppose in the U$.$S$.$ the median developer's salary can be approximated by

$S(x)=142-51(0\mathrm{.}9{)}^x$ thousand dollars,

where $x$ is the number of years of professional programming experience.

places.$)[$HINT: See Example $4.]$

For programmers in the U$.$S$.$ with between $15$ and $20$ years of professional programming experience, their median salary

at an average rate of about $

per additional year of

professional programming experience.

$($c$)$ Fill in the blank.

As her years of programming experience rises, a software developer's salary increases, but at a slower and slower rate $.$