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?

at 8:00 pm there will be 254 bacteria

Step-by-step 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