Answer:
Approximately 116.465 seconds after the chute opens.
Explanation:
To find the number of seconds after the chute opens when the skydiver will first be less than 100 feet in altitude, we need to set up and solve the equation H(x) < 100.
Given that H(x) = 3000 - 24.9x represents the altitude of the skydiver at time x seconds after the chute opens, we can rewrite the equation as follows:
3000 - 24.9x < 100
Now, we can solve this inequality to find the value of x:
3000 - 24.9x < 100
-24.9x < 100 - 3000
-24.9x < -2900
To isolate x, we divide both sides of the inequality by -24.9. However, we need to flip the inequality sign since we are dividing by a negative number:
x > (-2900) / (-24.9)
x > 116.465
Therefore, the skydiver will first be less than 100 feet in altitude after approximately 116.465 seconds after the chute opens.