Answer
The tendon has a Young's modulus of about $9.6*10^6N/m^2$
Work Step by Step
We can solve for Young's modulus, E, using the following formula:
$\Delta l=\frac{1}{E} \frac{F}{A}l_0$
$E=\frac{1}{\Delta l} \frac{F}{A}l_0$
$E=\frac{1}{0.0037m} \frac{13.4N}{\pi (1/2*0.0085m)^2}*0.15m$
$E\approx9.6*10^6N/m^2$
