A bacteria doubles its original population in 16 hours (A=2A0). How big will its population be in 96 hours?

Question

Applications of Exponential Equations

Use the exponential growth and decay models to find values other than the resultant value

Answer 1

Given that the bacteria doubles its original population in 16 hours, the formula for the growth of the bacteria is

A(t) = A₀2^(t/16), where A₀ is the original population and t is in hours.

A(96) = A₀2^(96/16) or

A(96) = A₀2⁶

A(96) = 64A₀

Thus, after 96 hours the bacteria population is 64 times the size of the original population.