SOLUTION: unsolved 2020-08-22 10:07:30 It is believed that two quantities, z and d are Connected by the relationship of the form z=kd^n where k and n are provided that d doesn't exceed some

Question 1163697: unsolved 2020-08-22 10:07:30 It is believed that two quantities, z and d are Connected by the relationship of the form z=kd^n where k and n are provided that d doesn't exceed some fixed (but unknown)values D.An experiment produced the following data
D 750 810 870 930 990 1050 1110 1170
Z 2.1 2.6 3.2 4.0 4.8 5.6 5.9 6.1
a)Plot the values of log10Z against log10 d.Use these points to suggest a
value for D.
b)It is known tht for d < D,n is a whole number.Use your graph to find the value of n.Show also that k=5×10^-9
c) Use your value of n and the estimate k=5×10^-9 to find the value of d for which z=3.0.
Answer by KMST(5342) (Show Source): You can put this solution on YOUR website!
If , then
The graph of against would be expected to be a straight line with slope up to a certain value .
We need to calculate and tabulate and

a)Then we plot against
The points in green, up to , corresponding to fit well enough on a line. That supports suggesting .

b) We could estimate as the slope between points

and

That slope is
Since is supposed to be a whole number, it must be .

c) For (rounded)
Substituting values for , , with and into we get

to get as the value of d for which z=3.0.
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