Spatial Exercise IV$\mathrm{.}3.$ For any positive real number $a,$

$a=e^{ln(a)},$ and $so,a{e}^x=e^{x+ln(a)}.$

$($a$)$ You and your friend are studying a quantity that is modeled by the function exp, but have difficulty because the function is so abrupt in how it changes$-$It is either very close to the $x$ axis, or appears to be nearly a vertical line. When you worked with polynomial functions, you found that you could scale the $y-$axis in order to better observe the growth of the polynomial over large intervals in the $x-$axis. Your friend suggests that you simply rescale the $y-$axis in order to better observe how the exponential function changes over a larger interval. What will happen if you do this?

$($b$)$ Sketch exp and then sketch $\frac{1}{1000}$ exp. How do these functions differ?