経済数学 II 練習問題 1 解答
1
(2) y = 2 × 712
log10 (2 × 712 ) = log10 2 + 12 × log10 7
= 0.301 + 12 × 0.845 = 10.441
(1) 2−3 × 24 = 2−3+4 = 21 = 2
(2) (2 3 )3 = 2 3 ×3 = 22 = 4
2
(3) 8− 3 = (8− 3 )2 = (
2
1
3
→ 11 桁
1
1
)2 = ( )2 =
2
4
8
1
1
3
1
(4) 25 2 = (25 2 )3 = 53 = 125
2
5
(5) 36 ÷ 6
3
10
2
5
= (6 ) ÷ 6
2
3
10
4
4
5
=6 ÷6
3
10
3
4
1
A = 2x2 − 1 とおくと
A dA
4x
f ′ (x) = d exp
dA
dx = 2x2 −1
(6) log27 1 = 0
f ′ (x) =
= −2
(9) log35 7 + log35 5 = log35 7 × 5 = log35 35 = 1
(10) log4
5
5
12 −log4 6
5
= log4 ( 12
× 65 ) = log4
1
2
= − 12
(11) log2 25 · log3 16 · log5 27
= log2 52 ×
log2 24
log2 3
= (2 × 4 × 3) ×
= 24
log2 33
log2 5
log2 2
log2 5 × log
23
×
×
log2 3
log2 5
= log 1 − log x2 = −2 log x
(3) f (x) = (x2 − x + 1)(x − 1) →省略
5
平均経済成長率
4
(1) ( 528,991.90
530,528.40 ) − 1 = −0.0115
→マイナス 1.15%
1
5
(2) ( 530,528.40
505,383.50 ) − 1 = 0.0098
(12) 2 log2 6 − log2 9 = log2
2
1
x2
− x2
(2) f (x) = log
(7) log3 27 = 3
1
4
指数関数・対数関数の微分
(1) f (x) = exp[2x2 − 1]
= 6 5 − 10 = 6 2
(8) log2
ねずみ算
(1) y = 2 × 7x
指数・対数の計算
2
3
62
9
= log2 4 = 2
複利
(1) A(1 + r)n
(2) (1 + 0.01)n = 2
log10 2
→ n = log1.01 2 = log
=
10 1.01
したがって，71 年。
(3) (1 + 0.05)n = 2
log10 2
→ n = log1.05 2 = log
=
10 1.05
したがって，15 年。
0.3010
0.0043
= 70.47
0.3010
0.0212
= 14.20
(4) (1.03)12 − 1 = 0.426 → 42.6%
(5) (1 + r)15 = 2
1
→ r = 2 15 − 1 = 0.0047 → 4.7%
1
(6) [(1 + 0.5) × (1 − 0.3)] 2 − 1 = 0.0247 → 2.47%
→ 0.98%

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Practice 4-4 Level B

数学Ⅱ