3.89: Logarithmic straightening of y=Abxy = Ab^x

0606/22/F/M/24 — Question 8 · 10 marks

Variables yy and xx are connected by y=Abxy = Ab^{x} where AA and bb are constants. The table shows values of yy for certain values of xx.
(a)
Draw the graph of lgy\mathrm{lg}\,y against xx.
[2]
(b)
Use your graph to find values of AA and bb, giving each to 11 significant figure.
[6]
(c)
Find an estimate of xx when y=1500y = 1500.
[2]