Question

An adventure sports club claims to take its hot air balloon to a height of 10,020 feet. The hot air balloon’s elevation is modeled by the equation y = x5 − 6x4 + 3x3 − 18x2 + 180x, where x is the number of minutes since the balloon took off. In how many minutes will the hot air balloon reach an elevation of 1,080 feet?
A)4 minutues
B)5 minutes
C)6 minutes
D)7 minutes

Answer 1

Answer: C) 6 minutes.

Step-by-step explanation: to solve the given problem we can replace the given option in the values of x, and calculate y for each option, the one that results in y=1080 feet will be the correct answer:

for option A:

$y=4^{5}-6*4^{4}+3 *4^{3}-18*4^{2} +180*4$

y=1024-1536+192-288+720

y=112 feet.

for option B:

$y=5^{5}-6*5^{4}+3 *5^{3}-18*5^{2} +180*5$

y=3125-3750+375-450+900

y=200 feet.

for option C:

$y=6^{5}-6*6^{4}+3 *6^{3}-18*6^{2} +180*6$

y=7776-7776+648-648+1080

y=1080 feet. As we can see the ballon will reach an elevation of 1080 feet in 6 minutes.

Answer 2

C, six minutes, it might be D idk