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Integration and Its Applications · Paper 2 — Free Maths AI HL Practice Questions

1MasterySAQ-SIndefinite integrals and their properties8 marksPaper 2~12 min
A company models the rate of change of its annual profit, PP million dollars, tt years after 2020 using the function P′(t)=12e−0.2t−3,t≥0.P'(t) = 12e^{-0.2t} - 3, \quad t \geq 0.
(a)
Find the general expression for P(t)P(t). [3 marks]
(b)
Given that the profit in 2020 was USD 5 million, determine the particular solution for P(t)P(t). [2 marks]
(c)
The company claims this model predicts long-term profit growth. By finding the value of tt at which P(t)P(t) is maximised and evaluating PP at that point, determine whether this claim is valid. [3 marks]
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