binomial 問題！ (20)

2009-03-28 3:33 am

8. The Acme Insurance Company sells two savings plans A and B.
For Plan A, an investor starts with an initial monthly deposit of $1000 and increases this by $80 each month, so that in the second month the deposit is $1090 and so on.
For Plan B, the investor starts with a monthly deposit of $1000 and each month deposits 6% more than the previous month.

(a) Write down the amount of money the investor deposits under the Plan B in the second and third months.

(b) Find the amount of the twelfth deposit for each plan, to the nearest dollar.

(c) Find the total amount of money invested during the first twelve months under each plan to the nearest dollar.

9. Expand each of the following in ascending powers of x up to and including the term in x 2
(a)( 1 + 2x )^5 (b) ( 1 – 3x )^10(c) ( 2 – 3x )^6

10. (a) Find the first four terms of the series(1 + 2x)^6 in ascending powers of x.

(b) By choosing a suitable value of and by using your expansion, find the value of 0.986 to four decimal places.

回答 (1)

vincent_kl_tam

2009-03-28 5:29 am

✔ 最佳答案

Do you mean “by $80 each month, so that in the second month the deposit is $1080 and so on”?
8a)Amount of money the investor deposits under the Plan B in the second month
=$1000*1.06
=$1060
Amount of money the investor deposits under the Plan B in the third month
=$1000*1.06²
=$1123.6
8b)Amount of the twelfth deposit for Plan A
=$1000+80(12-1)
=1880
Amount of the twelfth deposit for Plan B
=$1000+1.06¹¹
=$1900 (cor. to nearest dollar)
8c)Total amount of money invested during the first twelve months under Plan A
=$[1000*12+80(1+2+3+...+11)
=$17280
Total amount of money invested during the first twelve months under Plan B
=$(1000+1000*1.06¹+1000*1.06²+...+1000+1.06¹¹)
=$1000(1+1.06¹+1.06²+...+1.06¹¹)
=$1000(1.06¹²-1)÷(1.06-1)
=$16870 (cor. to nearest dollar)
9a)(1+2x)^5
=1+5(2x)+10(2x)²+...
=1+10x+40x²+...
9b)(1-3x)^10
=1-10(3x)+45(3x)²-...
=1-30x+405x²-...
9c)(2-3x)^6
=2^6-6(2)(3x)^5+15(2)²(3x)^4-...
=32-2916x+4860x²-...
10a)(1+2x)^6
=1+6(2x)+15(2x)²+20(2x)³+...
=1+12x+60x²+160x³+...
10b)Do you mean to find the value of 0.98^6 to 4 decimal places?
0.98^6
=(1-0.02)^6
=[1+2(-0.01)]^6
=1+12(-0.01)+60(-0.01)²+160(-0.01)³+...
=1-0.12+0.006-0.00016+...
=0.8858 (cor. to 4 d.p.)

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