a math problem

Giventhe data :
x=2，when y=50
x=6，when y=?
x=10，when y=288，for a functiony=f(x), predict y(6) if：
1. y is a linear function of x
Sol
y=ax+b
50=2a+b
288=10a+b
338=12a+2b
y(6)=6a+b=169

2. y is an exponential function of x
Sol
y=a*e^(bx)
50=a*e^(2b)
288=a*e^(10b)
50*288=(a^2)*(e^(12b)
14400=(a^2)*(e^(12b)
y(6)=a*e^(6x)=120

x=10, when y=288 , for a function y=f(x), predict y(6) if:

(288 – 50)/(10 – 2) = 238/8 = 29.75
Y = 29.75X + B
50 = 29.75(2) + B
50 – 59.5 = b
B = -9.5
y = 29.75v -9.5
y = 29.75(6) – 9.5
y = 169

y = ab^x

50 = ab^2
288 = ab^10
50/b^2 = 288/b^10
50b^10 = 288b^2
b^8 = 288/50
b^8 = 5.76
b = 1.24467
y = a(1.24467)^x
50 = a(1.24467)^2
a = 32.274
y = 32.274 (1.24467)^x
y = 32.274(1.24467)^6
y = 200

y = 169 when x = 6 for linear equation.

y = 200 when x = 6 for exponential equation.


2010-09-30 12:59:14 補充：
For linear equation, the slope is m = (y2-y1)/(x2 - x1) = (288 – 50)/(10 – 2) = 238/8 = 29.75

2010-09-30 13:08:12 補充：
Sorry that I pressed the wrong key of the calculator in my calculation,
Correction:

For exponent function:
y = 32.274(1.24467)^6
y = 120

y = 120 when x = 6 for exponential equation.