Answer:
a. y = 0.012x²
b. 4.80 m
c. 25 m/s
Explanation:
a. First, we need to determine what kind of function this is (linear, quadratic, etc.).
Logically, the function must pass through the origin, so we can compare the ratios between points.
Let's look at (5.00, 0.30) and (10.00, 1.20). When we double the speed, the depth quadruples. That tells us this must be a quadratic equation.
y = kx²
Plug in a point to find k:
0.30 = k (5.00)²
k = 0.012
Therefore, the equation is:
y = 0.012x²
We can check our answer by plugging in more points.
1.20 = 0.012 (10.00)²
2.70 = 0.012 (15.00)²
b. Find y when x = 20.00.
y = 0.012 (20.00)²
y = 4.80
c. Find x when y = 7.50.
7.50 = 0.012 x²
x = 25