A bacterial culture is observed to contain cells at 12:00 noon and cells at 4:00 p.m

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

A bacterial culture is observed to contain

5.0\times 10^{2}

cells at 12:00 noon and

2.0\times 10^{3}

cells at 4:00 p.m. Assume that the population grows exponentially. (i) Calculate the growth constant

k

(per hour) correct to four decimal places. (ii) Estimate the number of cells that will be present at 10:00 p.m. on the same day.