QuestionWatch VideoShow ExamplesThe position of an object moving in a straight line, in kilometers, can be modeled by the function s(t), where t is measured in days. The velocity of the object is 2 kilometers per day when t=5. Selected values of s(t) are shown in the table below. Use a linear approximation when t=5 to estimate the position of the object at time t=4.8. Use proper units.\begin{tabular}{|c|c|c|c|c|c|c|}\hlinet & 0 & 5 & 8 & 13 & 18 & 20 \\\hlines(t) & 30 & 40 & 55 & 80 & 90 & 100 \\\hline\end{tabular}
Q. QuestionWatch VideoShow ExamplesThe position of an object moving in a straight line, in kilometers, can be modeled by the function s(t), where t is measured in days. The velocity of the object is 2 kilometers per day when t=5. Selected values of s(t) are shown in the table below. Use a linear approximation when t=5 to estimate the position of the object at time t=4.8. Use proper units.\begin{tabular}{|c|c|c|c|c|c|c|}\hlinet & 0 & 5 & 8 & 13 & 18 & 20 \\\hlines(t) & 30 & 40 & 55 & 80 & 90 & 100 \\\hline\end{tabular}
Identify Given Values: Step 1: Identify the given values and the requirement.We know the velocity at t=5 is 2 km/day and we need to estimate the position at t=4.8 using linear approximation. We have s(5)=40 km from the table.
Calculate Change in Time: Step 2: Calculate the change in time.The change in time, Δt, from t=5 to t=4.8 is Δt=4.8−5=−0.2 days.
Use Velocity for Change in Position: Step 3: Use the velocity to find the change in position.Since the velocity at t=5 is 2 km/day, the change in position, Δs, can be approximated by Δs=velocity×Δt=2 km/day ×−0.2 days =−0.4 km.
Estimate Position at t=4.8: Step 4: Estimate the position at t=4.8. Using the change in position, estimate s(4.8)=s(5)+Δs=40km−0.4km=39.6km.
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