Answer
a.
$k=0.0211$
b.
$=38$ words
c.
$=54.3$ words
d.
$t=109.13$ minutes
Work Step by Step
$L(t)=A(1-e^{-kt})$
a. $L=20, A=200, t=5$
$L(5)=200(1-e^{-5k})=20,$
$0.1=1-e^{-5k},$
$e^{-5k}=0.9,$
$-5k=\ln {0.9},$
$k=0.0211$
b. $L(10)=200(1-e^{-0.0211\times10}),$
$=200(1-e^{-0.211}),$
$=38$ words
c. $L(15)=200(1-e^{-0.0211\times15}),$
$=200(1-e^{-0.3165}),$
$=54.3$ words
d. $180=200(1-e^{-0.0211\times t}),$
$0.9=(1-e^{-0.0211t}),$
$e^{-0.0211t}=0.1,$
$-0.0211t=\ln {0.1},$
$t=109.13$ minutes
