13. The path of a soccer ball can be modeled by h=-16 t^{2}+12 t+3, where h represents the height (in feet) of the ball after t seconds. At what time will the ball reach the ground? Round your answer to the nearest hundredth.

Step 1 ：The path of a soccer ball can be modeled by the equation \(h=-16 t^{2}+12 t+3\), where \(h\) represents the height (in feet) of the ball after \(t\) seconds. We want to find out at what time the ball will reach the ground.

Step 2 ：The ball reaches the ground when its height \(h\) is zero. So, we need to solve the equation \(-16t^2 + 12t + 3 = 0\) for \(t\).

Step 3 ：This is a quadratic equation, and we can solve it using the quadratic formula: \(t = [-b ± sqrt(b^2 - 4ac)] / (2a)\), where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation.

Step 4 ：In this case, \(a = -16\), \(b = 12\), and \(c = 3\). We only need the positive root, because time cannot be negative.

Step 5 ：Substituting the values of \(a\), \(b\), and \(c\) into the quadratic formula, we get two solutions for \(t\): \(t1 = 0.94782196186948\) and \(t2 = -0.19782196186947998\).

Step 6 ：Since time cannot be negative, we discard \(t2\) and round \(t1\) to the nearest hundredth to get \(t = 0.95\) seconds.

Step 7 ：Final Answer: The ball will reach the ground at \(\boxed{0.95}\) seconds.