Question

🔥 #7.%0D%0ATime, x (seconds)%0D%0ADepth of Person from Surface of Water, d(x) (feet)%0D%0A1%0D%0A−1.85%0D%0A4%0D%0A−7.28%0D%0A6%0D%0A−8.3%0D%0A8.5%0D%0A−6.65%0D%0A10%0D%0A−4.1%0D%0A11.5%0D%0A−0.38%0D%0ANeed help? Click here!%0D%0AA person dives into a pool from its edge to swim to the other side. The table shows the depth in feet of the person from the surface of the water after x seconds. The data can be modeled by a quadratic function.%0D%0A%0D%0A%0D%0A%0D%0AWhich function best models the data?%0D%0A%0D%0A%0D%0Adx=0.05x2+0.74x%0D%0A%0D%0Adx=0.05x2+0.74x+9.17%0D%0A%0D%0Adx=0.26x2−3.11x%0D%0A%0D%0Adx=0.26x2−3.11x+1

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which function best models the data, we need to analyze the given data points and see which function produces values closest to those in the table.

Let's first calculate the values for each function using the x-values in the table and then compare them to the corresponding y-values (depth) in the table.

For the first function:
d(x) = 0.05x^2 + 0.74x

Using x = 1: d(1) = 0.05(1)^2 + 0.74(1) = 0.05 + 0.74 = 0.79

Comparing to the actual value in the table, the difference is 0.79 - (-1.85) = 2.64

Repeat this process for the remaining data points for each function and compare the differences to determine which function best models the data.

After evaluating all the data points, it appears that the function:
dx = 0.26x^2 - 3.11x + 1

provides the values closest to the data points in the table.