Question

Jason is bungee jumping in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function y = x² - 18x, where x is the time in seconds and y is the height in feet.

A) How long did it take for Jason to reach his minimum height?


B) What was the lowest point that Jason reached?


C) Jason returned to the top of the bungee jump at what time?

Answer 1

A) 9 seconds

B) lowest point is -81 ft, or 81 ft below the top of the bungee jump

C) 18 seconds

Explanation:

A) To find the x-value of the turning point (minima/maxima) differentiate, then set to zero and solve for x:

`(dy)/(dx)=2x-18\\\\\implies (dy)/(dx)=0\\\\\implies 2x-18=0\\\\\implies x=9`

Therefore, it took 9 seconds to reach the minimum height

B) lowest point is when x = 9:

⇒ y = (9)² -18(9) = -81

Therefore, lowest point is -81 ft, or 81 ft below the top of the bungee jump

C) find x when y = 0

⇒ x² - 18x = 0

⇒ x(x - 18) = 0

⇒ x = 0 and x - 18 = 0

⇒ x = 0 and x = 18

So he returned to the top of the bungee jump at 18 seconds

Answer 2

A) 9 s

B) -81 feet

C) 18 feet

step by step explanation:

A)

`\sf y = x^2 - 18x`

use the vertex formula:
`\sf (-b)/(2a)`

Here a = -18 and a = 1, these are coefficients from ax² + bx + x

solve:

`\hookrightarrow \sf (--18)/(2(1))`

`\hookrightarrow \sf (18)/(2)`

`\hookrightarrow \sf 9` s

It takes 9 s for Jason to reach his minimum height.

B)

if taken 9 s then put it in x and find the height reached

`\sf \hookrightarrow \sf h(9) = 9^2 - 18(9)`

`\sf \hookrightarrow h(9) = 81 - 162`

`\hookrightarrow \sf h(9) = -81`

The lowest point is - 81 feet, as it says lowest.

C)

solve for when the height, y is 0

`\hookrightarrow \sf 0 = x^2 -18x`

`\hookrightarrow \sf 0 = x(x -18)`

`\hookrightarrow \sf x = 0, \ x -18 = 0`

`\hookrightarrow \sf x = 0, \ x = 18`

`\hookrightarrow \sf\ x = 18`

Jason returned to the top of the bungee jump at 18 s.