Answer
See an explanation
Work Step by Step
$U(t)=T+(u_0-T)e^{kt}, k\lt0,$
$U_0=72, T=38$
a. $U(2)=60=38+(72-38)e^{2k},$
$22=34e^{2k},$
$0.65=e^{2k},$
$\ln0.65=2k,$
$-0.2154=k,$
$U(7)=38+(72-38)e^{7(-0.2154)}=38+34e^{7\times -0.2154}=45.53$
b. $U(t)=38+(72-38)e^{-0.2154t}=39,$
$34e^{-0.2154t}=1,$
$-0.2154t=\ln{0.029},$
$t=16.4$
c. $U(t)=38+34e^{-0.2154t},$
$34e^{-0.2154t}=7,$
$-0.2154t=\ln{0.21},$
$t=7.34$
d. The temperature of the thermometer is decreasing as time passes to equal the temperature in the refrigerator.
