O-Level Exponential and logarithmic functions: worked solution

Question

Bacteria grow by N = a·10^(kt), t hours after the start. The data are t = 2,4,6,8 with N = 900, 2700, 8100, 24300. On the grid provided, plot lg N against t and draw the straight line of best fit.

N = a·10^(kt) so lg N = lg a + kt, a straight line of lg N against t. Compute lg N for each point: t=2, N=900: lg N = 2.95 t=4, N=2700: lg N = 3.43 t=6, N=8100: lg N = 3.91 t=8, N=24300: lg N = 4.39 Plot the four points (2, 2.95), (4, 3.43), (6, 3.91), (8, 4.39) on the grid and draw a single straight line of best fit through them (the points are collinear since N triples every 2 hours).