Question

if the number of bacteria in a colony doubles every 341 minutes and there is currently a population of 1,630 bacteria, what will the population be 1,705 minutes from now? bacteria

Explanation:

Step1: Calculate the number of doubling periods

The number of doubling periods \(n=\frac{1705}{341} = 5\)

Step2: Use the formula for exponential growth

The formula for population growth when it doubles is \(P = P_0\times2^n\), where \(P_0 = 1630\) and \(n = 5\)

Substitute the values: \(P=1630\times2^5\)

Since \(2^5=32\), then \(P = 1630\times32\)

\(P=1630\times32=(1600 + 30)\times32=1600\times32+30\times32=51200+960 = 52160\)

Answer:

\(52160\)