Answer:
The time duration of the ocra whale spends under water is 4 seconds
Step-by-step explanation:
The equation that model the path of the ocra whale is presented as follows;
k(x) = x² - 2·x - 8
Where;
x = The time elapsed in seconds under water
k(x) = The height in feet below water
Therefore, the point where the ocra whale enters the water, k(x) = 0
At the point of submerging below the water surface, we have;
k(x) = 0 = x² - 2·x - 8
Factorizing the quadratic equation gives;
0 = x² - 2·x - 8 = (x - 4)·(x + 2)
Therefore, when k(x) = 0, either;
(x - 4) = 0, which gives, x = 4
(x + 2) = 0, which gives, x = -2
Given that 'x' represent the time, the time elapsed while the whale is under water, x = 4 seconds
