Ryan has the chickenpox! He was told that the number of pockmarks on his body would grow exponentially until his body overcomes the illness. He counted $60$ pockmarks on November 1 and by November 3 the number had grown to $135$. To determine when the first pockmark appeared, he needs to write the exponential function that models the number of pockmarks based on the date in November.

1. Ryan decides to use the points $\left(1, 60\right)$ and $\left(3, 135\right)$ to write an equation for the exponential model. Use these points to write the equation of his function in the form $y = ab^{x}$.

   Hint (a):

   Substitute both points into the equation $y = ab^{x}$ and solve for $a$ and $b$.

   Answer (a):

   $y = 40\left(1.5\right)^{x}$

2. According to your model, on what day did Ryan get his first chickenpox pockmark?

   Step 1(b):

   Solve for $x{:}\ 1=40\left(1.5\right)^x$

   Answer (b):

   $x = −9$, so October 22