Sometimes we want the initial response to be a bit more flat, then rise up to the final response, and then be more flat. A slight variation on the previous formula works well. These are often called Hill functions and you'll see a lot of their graphs in BIO$152$ during the circulatory system.

Consider $g(x)=\frac{60x^2}{4^2+x^2}$

What is $g(0)=$

What is the largest value of $g?$ What is the final value? What is $g(1000),$ feel free to round$-$off:

When is it half$-$way from $0$ to $60?$ When $x=$

Look at the difference in the graphs of $f$ and $g.$ Use an online grapher like desmos

it is not $6\mathrm{.}48$ or $15\mathrm{.}55$