The amount of water in a tank, in liters, can be modeled by the function Q(t), where t is measured in hours. The instantaneous rate of change of the amount of water in the tank is 4 liters per hour when t=5. Selected values of Q(t) are shown in the table below. Use a linear approximation when t=5 to estimate the amount of water in the tank at time t=5.1. Use proper units.\begin{tabular}{|c|c|c|c|c|c|}\hlinet & 0 & 5 & 7 & 10 & 15 \\\hlineQ(t) & 31 & 51 & 41 & 26 & 11 \\\hline\end{tabular}Answer kempricet ofs
Q. The amount of water in a tank, in liters, can be modeled by the function Q(t), where t is measured in hours. The instantaneous rate of change of the amount of water in the tank is 4 liters per hour when t=5. Selected values of Q(t) are shown in the table below. Use a linear approximation when t=5 to estimate the amount of water in the tank at time t=5.1. Use proper units.\begin{tabular}{|c|c|c|c|c|c|}\hlinet & 0 & 5 & 7 & 10 & 15 \\\hlineQ(t) & 31 & 51 & 41 & 26 & 11 \\\hline\end{tabular}Answer kempricet ofs
Identify Rate of Change: Identify the rate of change at t=5, which is given as 4 liters per hour. This means for every hour, the amount of water changes by 4 liters.
Use Value at t=5: Use the value of Q(t) at t=5 from the table, which is 51 liters.
Calculate Change: Since the rate of change is 4 liters per hour, and we need to find the amount at t=5.1, we calculate the change over 0.1 hours. The change in water amount =4 liters/hour ×0.1 hours =0.4 liters.
Estimate Amount at t=5.1: Add this change to the amount at t=5 to estimate the amount at t=5.1. So, Q(5.1)≈51 liters+0.4 liters=51.4 liters.
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