Linear Law Ex1

1.

Variables and are known to be related by an equation of the form

, where and are constants. Observed values of the two variables are shown n the following table.

   1  2  3  4
   4.00  2.50  2.67  3.25

Plot against and use the graph to estimate

(a) the value of when = 1.5,

(b) the value of and .

Solutuion:

   1  2  3  4
   4.00  2.50  2.67  3.25
   3.00  1.00  -0.99  -3.00

2.

The table shows experimental values of the variables and .

   2  3  4  5  6
   11.9  21.2  32.0  44.1  57.4

It is known that and are related by the equation , where and are constants.

(a) Express the equation in a form suitable for drawing a straight line graph.

(b) Draw the graph and use it to estimate the value of and of .

(c) With the estimated values of and , calculate the value of when .

Solutuion:

(b)

   2  3  4  5  6
   11.9  21.2  32.0  44.1  57.4
   1.00  1.26  1.45  1.59  1.71
   0.30  0.48  0.60  0.70  0.78