Question

A section of a water tube ride at an amusement park can be modelled by the function h(t)=−0.002t^4 +0.104t^3​​ −1.69t^2 +8.5t +9 where t is the time, in seconds, and h is the height, in metres, above the ground. When will the riders be more than 15 m above the ground?

Answer 1

The riders will be more than 15 m above the ground when the given water tube ride function is greater than 15.

Step-by-step explanation:

The given model of the water tube ride can be represented by the function h(t) = -0.002t4 + 0.104t3 - 1.69t2 + 8.5t + 9, where t is the time in seconds and h is the height in meters above the ground.

To find when the riders will be more than 15 m above the ground, we need to solve the inequality h(t) > 15.

By substituting the function into the inequality, we get -0.002t4 + 0.104t3 - 1.69t2 + 8.5t + 9 > 15.

This inequality can be solved either graphically or numerically to find the time t when the riders will be more than 15 m above the ground.