(1 point)
A factory produces bicycles at a rate of $105+0.5 t^{2}-0.9 t$ bicycles per week ( $t$ in weeks). How many bicycles were produced from day 15 to 28 ?
Answer: $\square$ bicycles. (Note: Round down to the nearest whole number since a factory only produces whole bicycles.)
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Answer
The total number of bicycles produced from day 15 to day 28 is \(\boxed{198}\) bicycles
Step 1 ：Convert days to weeks: Day 15 is equivalent to \( \frac{15}{7} \) weeks and day 28 is equivalent to \( \frac{28}{7} \) weeks
Step 2 ：Calculate the definite integral of the rate function from \( \frac{15}{7} \) to \( \frac{28}{7} \) to find the total number of bicycles produced
Step 3 ：Round down the result to the nearest whole number since a factory only produces whole bicycles
Step 4 ：The total number of bicycles produced from day 15 to day 28 is \(\boxed{198}\) bicycles
