Question

The population of an idealized colony of bacteria grows exponentially, so that the population doubles every half-hour. The experiment begins at 6:00pm. If at 6:10pm the population is measured at 20 bacteria, how many will there be at 8:00pm?

Answer 1

at 8:00 pm there will be 254 bacteria

Explanation:

the equation governing the population of the colony N in function of time t is

N(t)=N₀*2^(t/30) , where t is in minutes from 6:00 pm , and N₀ is the initial population

thus for t₁=6:10 pm = 10 min from 6:00 pm and t₂=8:00 pm=120 min from 6:00 pm , we have

N₁=N₀*2^(t₁/30)

N₂=N₀*2^(t₂/30)

dividing both equations

N₂/N₁=2^(t₂/30-t₁/30)

N₂ = N₁*2^[(t₂-t₁)/30]

replacing values

N₂ = N₁*2^[(t₂-t₁)/30] = 20 bacteria * 2^[(120 min-10 min)/30] =253.98 ≈ 254 bacteria

then at 8:00 pm there will be 254 bacteria