Question

The voltage of a cell remains constant at 70 mV for any stimulus less than 70 mV. If it receives a voltage greater than 70 mV the voltage in the cell is proportional to the stimulus voltage with voltage in the cell equal to 105 mV when the stimulus is 70 mV. Write a formula for the function V(s), the voltage in the cell given stimulus voltage s mV.

Answer 1

Since the voltage in the cell is V(s), where s is the stimulus voltage

If s is less than 70 mv, then V(s) = 70 mv

If s is greater than 70, then V(s) = ks

To find the value of k, substitute v(s) by 105 mv and s by 70 mv

$\begin{gathered} 105=k(70) \\ 105=70k \end{gathered}$

Divide both sides by 70

$\begin{gathered} \frac{105}{70}=\frac{70k}{70} \\ 1.5=k \end{gathered}$

Then the equation is

$V(s)=1.5k$

The answer is V(s) = 1.5 s