Math $110$

Fall $2024$

Chain rule applications

The percentage of mothers who work outside the home and have children younger than age $6$ is approximated by the function

$P(t)=33\mathrm{.}55(t+5{)}^{0\mathrm{.}205},(0t21)$

where $t$ is measured in years with $t=0$ corresponding to the beginning of $1980.$

a$.$ What was the percentage of mothers working outside the home at the beginning of $2000?$

b$.$ Compute $P^{\text{'}}(t)$

c$.$ At what rate was the percentage of these mothers changing at the beginning of $2000?$

d$.$ Compute $P^{\text{'}\text{'}}(20)$ and interpret your results.