3.34: Linear law: lg⁡P\lg P against TT for P=AbTP=Ab^{T}

0606/22/M/J/23 — Question 5 · 9 marks

3.34 diagram
(a)
Variables PP and TT are connected by P=AbTP=Ab^{T}. Show that a graph of lg⁡P\lg P against TT will be a straight line.
[2]
(b)
The diagram shows the graph of lg⁡P\lg P against TT through (0,6)(0, 6) and (14,12)(14, 12). Find the values of AA and bb.
[4]
(c)
Find the length of time for which PP is between 100100 million and 10001000 million.
[3]