Question

1. a cell culture starts with 500 cells and doubles every 6 hours. find the population after 18 hours.

Explanation:

Step1: Calculate the number of doubling periods

The time period is \(18\) hours and it doubles every \(6\) hours. So the number of doubling periods \(n=\frac{18}{6}=3\).

Step2: Use the formula for population growth

The initial population \(P_0 = 500\). The formula for population growth when it doubles is \(P = P_0\times2^n\). Substitute \(P_0 = 500\) and \(n = 3\) into the formula: \(P=500\times2^3\).
Calculate \(2^3=8\), then \(P = 500\times8\).

Answer:

\(4000\)