# For f(t)= (lnt/e^t, te^t) what is the distance between f(1) and f(2)?

Apr 14, 2017

$d \approx 12.06$

#### Explanation:

First, plug in $1$:

$f \left(1\right) = \left(\ln \frac{1}{e} ^ 1 , 1 \left({e}^{1}\right)\right)$

$f \left(1\right) = \left(0 , {e}^{1}\right)$

Now plug in $2$:

$f \left(2\right) = \left(\ln \frac{2}{e} ^ 2 , 2 \left({e}^{2}\right)\right)$

Now use the distance formula:

$d = \sqrt{{\left(\ln \frac{2}{e} ^ 2 - 0\right)}^{2} + {\left(2 {e}^{2} - {e}^{1}\right)}^{2}}$

$d \approx 12.06$