Question

What’s is the inverse function of a(m)=0.6735e^0.423m

Answer 1

Answer:

$a^{-1}(m)=\frac{ln(\frac{m}{0.6735})}{0.423}$

Step-by-step explanation:

The function is  $a(m)=0.6735e^{0.423m}$

Changing functional notation of a(m) to y:

$y=0.6735e^{0.423m}$

Now, interchanging m and y:

$m=0.6735e^{0.423y}$

Now, solving for y:

$e^{0.423y}=\frac{m}{0.6735}\\ln[e^{0.423y}]=ln[\frac{m}{0.6735}]\\0.423y=ln(\frac{m}{0.6735})\\y=\frac{ln(\frac{m}{0.6735})}{0.423}$

Thus, the inverse function is:

$a^{-1}(m)=\frac{ln(\frac{m}{0.6735})}{0.423}$