O-Level Exponential and logarithmic functions: worked solution

Question

For two quantities R and t the recorded pairs (t, R) are (20, 2.79), (10, 2.32), (40, 4.74), (30, 3.31) and (50, 4.90), and they obey R = R₀(3^(-kt)) with one R mis-recorded. Plot ln R against t and draw the straight line that fits.

R = R₀·3^(−kt) so ln R = ln R₀ − kt ln 3, a straight line of ln R against t. Compute ln R: t=10, R=2.32: ln R = 0.84 t=20, R=2.79: ln R = 1.03 t=30, R=3.31: ln R = 1.20 t=40, R=4.74: ln R = 1.56 t=50, R=4.90: ln R = 1.59 Plot (10, 0.84), (20, 1.03), (30, 1.20), (40, 1.56), (50, 1.59) and draw the straight line of best fit ignoring the one mis-recorded (outlying) point.