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Free response·Hard exam skill (4/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

A pond initially contains 18001800 fish. Fish enter the pond at rate E(t)=30+4tE(t)=30+4t fish/day and leave at rate L(t)=12+2tL(t)=12+2t fish/day for 0≤t≤10.0\le t\le10.
Total: 5 points

(a) Write an expression for the number of fish in the pond at time tt. (2 points)

(b) Find the number of fish in the pond at t=10t=10. (1 point)

(c) Find the average net rate of change of the fish population on [0,10][0,10]. (1 point)

(d) Is the number of fish increasing throughout the interval? Justify your answer. (1 point)

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