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 found that he had $60$ pockmarks on November 1, and by November 3 the number had grown to $135$. To find out when the first pockmark appeared, he will need to find the exponential function that will model the number of pockmarks based on the day.

1. Ryan decides to find the exponential function that passes through the points $(3,135)$ and $(1,60)$. Use these points to write the equation of his function of the form $f\left(x\right)=ab^x$.

   Hint (a):

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

   Answer (a):

   $y=40(1.5)^x$

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

   Answer (b):

   $x=−9$, or October 22