根据利息理论，已知 A(t)=2t+\sqrt{t}+5，求:(1)对应的 a(t);(2)I_{3};(3)i_{4}

根据利息理论，有：

(1) a(t) = A'(t) = 2 + 1/(2√t)

(2) I_3 = ∫[2, 3] a(t) dt = ∫[2, 3] (2 + 1/(2√t)) dt = [2t + √t]_2^3 + [ln(√t)]_2^3

= (2(3) + √3) - (2(2) + √2) + ln(3/√3) - ln(2/√2)

≈ 4.03

(3) i_4 = a(4) = 2 + 1/(2√4) = 2.25