To find the initial height of the bird in the tree using the given equation \( y = 36.79x^2 - 59.66x + 24.19 \), we need to evaluate the equation when \( x = 0 \) (which represents the initial time).
Plugging \( x = 0 \) into the equation, we get:
\[ y = 36.79(0)^2 - 59.66(0) + 24.19 \] \[ y = 0 - 0 + 24.19 \] \[ y = 24.19 \]
So, the initial height of the bird in the tree is \( 24.19 \) feet. Rounding this to the nearest tenth gives us \( 24.2 \) feet.
Thus, the correct answer is:
24.2 feet