1條數學請教

1a
設(x,y)=(-1,2.5) (x1,y1)=(3,8.5)

2.5=-a+b 1
8.5=3a+b 2
2-1
4a=6
a=1.5

a=1.5 put into 1
2.5=-(1.5)+b
b=4
so(a,b)=(1.5,4)

1b
logy=ax+b
logy=1.5x+4
y=10^(1.5x+4)

1c
x=-4
y=10^(1.5*-4+4)
y=0.01

x和logy的關係可用公式logy=ax+b表示,其中a和b為常數.圖中所示為logy對x的圖像,圖像通過(-1,2.5)和(3,8.5).

(a) 求a和d的值.
For (-1, 2.5),
2.5 = a(-1) + b
2.5 = -a + b ----------------(1)

For (3, 8.5)
8.5 = a(3) + b
8.5 = 3a + b --------------- (2)

Two simultaneous linear equations, solve for the unknwn a and b.
(2) – (1)
3a – (-a) = 8.5 – 2.5
4a = 6
a = 6/4 =1.5
8.5 = 3(1.5) + b
b = 8.5 - 3(1.5) = 4

a = 1.5 and b = 4

(b)試以x表示y.

logy=ax+b
y = 10^(ax +b)
if a = 1.5 and b = 4

y = 10^(1.5x +4)

(c) 求當x=-4時y的值.

y = 10^(1.5x +4)
y = 10^(1.5(4) +4)
y = 10^(6+4)
y = 10^(10)
y = 10,000,000,000