To find the initial height of the bird in the tree, we need to evaluate the equation \( y = 36.79x^2 - 59.66x + 24.19 \) at \( x = 0 \) seconds (the initial time).
Let's substitute \( x = 0 \) into the equation:
\[ y = 36.79(0)^2 - 59.66(0) + 24.19 \]
Now, simplifying the equation:
\[ y = 0 - 0 + 24.19 \] \[ y = 24.19 \]
So, the initial height of the bird in the tree is \( 24.19 \) feet. Rounding to the nearest tenth gives us:
\[ 24.2 \text{ feet} \]
Thus, the correct response is \( \text{24.2 feet} \).