Question

Inverse of A=300e^-0.013t

Answer 1

`A^(-1)(t)=-(ln((t)/(300)))/(0.013)`

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

`(t)/(300)=e^(-0.013A)`

Apply ln (natural logarithm) both sides

`ln((t)/(300))=ln[e^(-0.013A)]`

`ln((t)/(300))=(-0.013A)ln(e)`

Remember that

`ln(e)=1`

`ln((t)/(300))=(-0.013A)`

`A=-(ln((t)/(300)))/(0.013)`

Let

`A^(-1)(t)=A`

so

`A^(-1)(t)=-(ln((t)/(300)))/(0.013)`