Help ~數統2問

2009-11-08 8:02 pm

希望大家可以幫幫忙,教教我^^ 請詳盡地列式~thx!!

1) The figure above shows a straight line graph of Iny against Inx. The line cuts
the axes at A(0,2) and B(4,0).

What is the equation connecting x and y?

2) When a softdrink is not advertised, its sales S will fall and follow the
equation S = S0 e^(-0.12t)
Where t is the number of months without advertising and S0 is a constant.

(a) How long will it take for the sales to
(i) reduce to half ?
(ii) diminish to 30% of the original amount ?
Give your answers correct to the nearest 0.1 moth.

(b) After no advertising for 6 months, there is an advertising campaign.
Then the sales grows according to the equation S=A e^(0.08t)
Where t is the number of months after the commencement of the
campaign and A is a constant. When will the sales resume to S0?

回答 (1)

myisland8132

2009-11-08 8:50 pm

✔ 最佳答案

1 By the information given, the slope of the graph is (0-2)/(4-0)=-1/2
So, (lny-2)=(-1/2)(lnx)
-2(lny-2)=lnx
2-lny=lnx
e^(2-lny)=x
e^2/y=x
xy=e^2
2(a)(i) Sub. S=S0/2.
1/2=e^(-0.12t)
ln(1/2)=-0.12t
t=ln2/-0.12
t=5.8
(ii) Sub. S=0.3S0.
0.3=e^(-0.12t)
ln(0.3)=-0.12t
t=ln(0.3)/-0.12
t=10.0
(b) Sub. t=0 and S=S0e^(-0.12*6)=S0e^(-0.72)
S0e^(-0.72)=A
Now let S=S0=>S0=S0e^(-0.72)e^(0.08t)
e^(0.08t-0.72)=1
0.08t=0.72
t=9
After nine months of the campaign the sales will resume to S0

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