Answer:
[tex]a^{-1}(m)=\frac{ln(\frac{m}{0.6735})}{0.423}[/tex]
Step-by-step explanation:
The function is [tex]a(m)=0.6735e^{0.423m}[/tex]
Changing functional notation of a(m) to y:
[tex]y=0.6735e^{0.423m}[/tex]
Now, interchanging m and y:
[tex]m=0.6735e^{0.423y}\\[/tex]
Now, solving for y:
[tex]e^{0.423y}=\frac{m}{0.6735}\\ln[e^{0.423y}]=ln[\frac{m}{0.6735}]\\0.423y=ln(\frac{m}{0.6735})\\y=\frac{ln(\frac{m}{0.6735})}{0.423}[/tex]
Thus, the inverse function is:
[tex]a^{-1}(m)=\frac{ln(\frac{m}{0.6735})}{0.423}[/tex]
