Exponential Transpose Problem

Question

hi am having problems transposing:v= 5 + 75/1+e^-(t-50)/10 to make t the subject.. i have tried everything but cannot replicate the inverse function to give me the correct graph. Can you help..?

Answer 1

Assuming that v= 5 + 75/(1+e^-((t-50)/10))

 

Replace v and t and you get

t= 5 + 75/1+e^-((v-50)/10)

then solve it for v

 

subtract 5 from both sides, multiply by 1+e^-((v-50)/10) and divide by (t-5)

you get

1+e^-((v-50)/10)=75/(t-5)

 

Subtract 1 from both sides and take natural log of both sides and you get

-((v-50)/10=ln(((75/(t-5))-1)

 

Multiply by -10 and then add 50

 

and you end up with 

 

v=50-10ln(((75/(t-5))-1)