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AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 8

Lesson 3: Using accumulation functions and definite integrals in applied contexts

Interpreting definite integrals in context

AP.CALC: CHA‑4 (EU), CHA‑4.D (LO), CHA‑4.D.1 (EK), CHA‑4.D.2 (EK), CHA‑4.E (LO), CHA‑4.E.1 (EK)

The population of a town grows at a rate of r, left parenthesis, t, right parenthesis people per year (where t is time in years). At t, equals, 3, the town's population was 1000 people.

What does 1000, plus, integral, start subscript, 3, end subscript, start superscript, 8, end superscript, r, left parenthesis, t, right parenthesis, d, t, equals, 1500 mean?

(Choice A)
The average rate at which the population grew between t, equals, 3 and t, equals, 8 is 1500 people per year.
(Choice B)
The town's population grew by 1500 people between t, equals, 3 and t, equals, 8.
(Choice C)
The town's population grew at a rate of 1500 people per year at t, equals, 8.
(Choice D)
At t, equals, 8, the town's population was 1500 people.

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AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 8

Problem