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7-35.

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. Homework Help ✎

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 $y = ab^{x}$.

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

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

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

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

$x = −9$, so October 22