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

Answer 1

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