Question

Inverse of A=300e^-0.013t

Answer 1

Answer:

$A^{-1}(t)=-\frac{ln(\frac{t}{300})}{0.013}$

Step-by-step explanation:

we have

$A=300e^{-0.013t}$

Exchange the variables A for t and t for A

$t=300e^{-0.013A}$

Isolate the variable A

$\frac{t}{300}=e^{-0.013A}$

Apply ln (natural logarithm) both sides

$ln(\frac{t}{300})=ln[e^{-0.013A}]$

$ln(\frac{t}{300})=(-0.013A)ln(e)$

Remember that

$ln(e)=1$

$ln(\frac{t}{300})=(-0.013A)$

$A=-\frac{ln(\frac{t}{300})}{0.013}$

Let

$A^{-1}(t)=A$

so

$A^{-1}(t)=-\frac{ln(\frac{t}{300})}{0.013}$