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Question
In a newly developed city, it is estimated that the voting population (in thousands) will increase according to V(t) = 30 + 12t2 – t3, 0 ≤ t ≤ 8 where t is the time in years. Find the approximate change in voters for the time change from 4 to `4 1/6` years
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Solution
V(t) = 30 + 12t2 – t3
dt = `4 1/6 - 4 = 1/6`
V’(t) = (24t – 3t2)dt
= `(24(4) - 3(4)^2) xx 1/6`
= `(96 - 48) xx 1/6`
= `48 xx 1/6`
= 8
Voters in thousands
∴ Approximate change of voters = 8 × 1000 = 8000
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