In spring $2020,$ the total number of Covid$-19$ cases in the US was growing exponentially with a

doubling time of about $3$ days. ${?}^1$

Round your answers to $2$ decimal places.

$($a$)$ Someone says that since the number of cases grows by $100\%$ in $3$ days, the daily growth rate

is $100\frac{\%}{3}=33\mathrm{.}33\%.$ Explain why this is not correct by computing the $3-$day growth factor of a

quantity that grows $33\mathrm{.}33\%$ per day.

Daily growth of $33\mathrm{.}33\%$ corresponds to a growth factor of

In other words, daily growth of $33\mathrm{.}33\%$ corresponds to a

i

$\%$ increase over $3$ days.

This is

:han a $100\%$ increase.

$($b$)$ Find the daily growth rate of a quantity that doubles every $3$ days.

Daily growth rate $=$

$\%$

${?}^1$ Smoothed from JHU CSSE COVID$-19$ data at

github.com$/$CSSEGISandData$/$COVID$-19,$

accessed June $10,2020.$