A model rocket is launched with an initial upward velocity of $204\mathrm{ft}/\mathrm{s}$. The rocket's height $h$ (in feet) after $t$ seconds is given by the following
$$h=204t-16t^2$$
Find all values of $t$ for which the rocket's height is 100 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

Step 1 ：We are given a model rocket is launched with an initial upward velocity of 204 ft/s. The rocket's height h (in feet) after t seconds is given by the equation $h=204t-16t^2$. We need to find all values of t for which the rocket's height is 100 feet.

Step 2 ：This means we need to solve the equation $204t-16t^2=100$ for t. This is a quadratic equation.

Step 3 ：We can solve it using the quadratic formula $t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, where a = -16, b = 204, and c = -100.

Step 4 ：Substituting the values of a, b, and c into the quadratic formula, we get two solutions for t.

Step 5 ：The solutions are t = 0.51 seconds and t = 12.24 seconds.

Step 6 ：Final Answer: The rocket's height is 100 feet at $t=\boxed{{\displaystyle 0.51}}$ seconds or $t=\boxed{{\displaystyle 12.24}}$ seconds.