Hello, i was wondering if e^(2t) is equivalent to e^(t^2). I cant seem to find if this is true or not.

Question

Thanks

Answer 1

e^(2t) is equal to e^(t^2) if and only if t=2 or t=0, simply because 2t=t² for these two values of t.

Since in general, 2t≠t², e^(2t) is not equivalent to e^(t^2).

For example, t=4,
e^2t=e⁸=2980.96
e^t²=e¹⁶=8886110.52

The confusion arises probably because
e^2t=(e^t)²
while
e^t²=(e^t)^t

Hope that clears it up.