Problem
Name: 5. The function $Q=0.003 t^{2}-0.625 t+25$ represents the amount of energy, in Joules, in a battery after t minutes of use. a) State the amount of energy held by the battery immediately before it was used. [1] \[ \begin{aligned} Q & =0.003 t^{2}-0.625 t+25 \\ & =0.003(0)^{2}-0.625(0)+25 \\ Q & =25 \end{aligned} \] b) Calculate the number of minutes it takes for the energy to reach zero. [4]
Solution
Step 1 ：\(Q = 0.003 t^{2} - 0.625 t + 25\)
Step 2 ：\(Q = 0.003(0)^{2} - 0.625(0) + 25\)
Step 3 ：\(Q = 25\)
Step 4 ：\(0 = 0.003t^2 - 0.625t + 25\)
Step 5 ：\(t \approx 53.99\)
Step 6 ：\(\boxed{\text{a) 25 Joules}}\)
Step 7 ：\(\boxed{\text{b) 53.99 minutes}}\)
