interpolating data\nheather is training for a long - distance run. her data points listed below represent…

interpolating data\nheather is training for a long - distance run. her data points listed below represent the days of practice, x, and the number of miles run, y.\n(1, 2.5), (2, 4.2), (4, 5.6), (6, 7), (8, 8.1), (10, 11)\nuse the equation to interpolate the value and estimate the distance that she could have run on day 3. round to the nearest tenth of a mile.\nday 3 ≈ 4.9 miles

interpolating data\nheather is training for a long - distance run. her data points listed below represent the days of practice, x, and the number of miles run, y.\n(1, 2.5), (2, 4.2), (4, 5.6), (6, 7), (8, 8.1), (10, 11)\nuse the equation to interpolate the value and estimate the distance that she could have run on day 3. round to the nearest tenth of a mile.\nday 3 ≈ 4.9 miles

Answer

Explanation:

Step1: Identify adjacent points

Adjacent to x=3: (2,4.2) and (4,5.6)

Step2: Apply linear interpolation formula

$y = 4.2 + (3-2)\cdot\frac{5.6-4.2}{4-2}$

Step3: Compute slope

$\frac{5.6-4.2}{4-2} = 0.7$

Step4: Calculate y at x=3

$y = 4.2 + 1\cdot0.7 = 4.9$

Answer:

4.9