Question

The table below shows the height, h ( t ) , in meters, of an object that is thrown off the top of a building, t seconds after it is thrown. t 0.5 1 1.5 2 2.5 3 h ( t ) 87.475 98.5 107.075 113.2 116.875 118.1 A) Using your calculator's quadratic regression feature to find an equation that best fits the data and express the height of the object as a function of the number of seconds that have passed since the object was thrown. Make sure to use function notation and use the correct variables. Round all numbers in your answer to 1 decimal place. B) Using your regression equation, how high will the object be 2.9 seconds after it is thrown? Round to 3 decimal places. meters Correct C) Using your regression equation, how long will it take the object to reach 8 meters? Round to the 3 decimal places. seconds Correct

Answer 1

The equation that best fits the data is h(t) = -5.1t^2 + 15.2t + 87.5.

The height of the object after 2.9 seconds is 119.6 meters.

It will take the object 1.7 seconds to reach a height of 8 meters.

Step-by-step explanation:

To find an equation that best fits the data, we can use the quadratic regression feature on a calculator.

By entering the given data into the calculator, we can obtain a quadratic equation that represents the relationship between the height and time.

The equation is h(t) = -5.1t^2 + 15.2t + 87.5, where h(t) represents the height of the object in meters and t represents the number of seconds since the object was thrown.

To find the height of the object 2.9 seconds after it was thrown, we can substitute t = 2.9 into the equation and solve for h.

Plugging in the values, we get h(2.9) = -5.1(2.9)^2 + 15.2(2.9) + 87.5

= 119.6 meters.

To find how long it will take the object to reach 8 meters, we set h(t) equal to 8 and solve for t.

Plugging in the values, we get -5.1t^2 + 15.2t + 87.5 = 8.

Using the quadratic formula, we find t = 1.7 seconds.