Answer:
18.6
Step-by-step explanation:
We are given that
[tex]22=32e^{-0.02k}[/tex]
We have to find the value of k.
Divide by 32 on both sides then we get
[tex]\frac{22}{32}=e^{-0.02k}[/tex]
[tex]\frac{11}{16}=e^{-0.02k}[/tex]
Taking ln on both sides then we get
[tex]ln\frac{11}{16}=-0.02k[/tex]
[tex]lne=1[/tex]
[tex]ln11-ln16=-0.02k[/tex]
[tex]log\frac{m}{n}=logm-logn[/tex]
[tex]2.398-2.77=-0.02k[/tex]
[tex]-0.372=-0.02k[/tex]
[tex]k=\frac{-0.372}{-0.02}=18.6[/tex]
Hence, the value of k=18.6
