A Wicked Witch of the West monitors the rate at which thousands of flying monkeys return to her dark castle after a day of terrorizing tin men and scarecrows. The busiest period usually occurs between 5 PM and 5:30 PM, since the winged simians get their monkey chow at 5:30 PM sharp. The witch determines that the rate M(t) at which monkeys enter the castle is modeled well by the formula M(t) = 60 +0.9t-0.003t3 monkeys per minute (mpm), where t is the time in minutes since 5 PM. At what time of day do the monkeys reach an absolute maximum flow rate into the castle and what is the absolute max flow rate? Determine the number of monkeys that enter the castle during the 30-minute period.
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Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
A Wicked Witch of the West monitors the rate at which thousands of flying
monkeys return to her dark castle after a day of terrorizing tin men and scarecrows. The busiest period usually occurs between 5 PM and 5:30 PM, since the winged simians get their monkey chow at 5:30 PM sharp. The witch determines that the rate M(t) at which monkeys enter the castle is modeled well by the formula M(t) = 60 +0.9t-0.003t3 monkeys per minute (mpm), where t is the time in minutes since 5 PM.
- At what time of day do the monkeys reach an absolute maximum flow rate into the castle and what is the absolute max flow rate?
- Determine the number of monkeys that enter the castle during the 30-minute period.
- If the model holds true until every monkey returns, how many monkeys arrive late and miss the 5:30 PM feeding and go to bed hungry? Round to the nearest monkey.
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