The initial population is 250 bacteria, and the population after 9 hours is double the population after 1 hour. How many bacteria will there be after 5 hours?

Question

Eva Adamson · Accepted Answer

undefined To find the population after 5 hours, we can use the concept of exponential growth. Since the population doubles every hour, we can set up the equation: $ P(t) = P_0 \times 2^{t} $, where $ P(t) $ is the population at time $ t $, $ P_0 $ is the initial population, and $ t $ is the time in hours.

Given that the initial population ($ P_0 $) is 250 bacteria, we can calculate the population after 1 hour: $ P(1) = 250 \times 2^{1} = 500 $ bacteria.

Now, to find the population after 5 hours, we substitute $ t = 5 $ into the equation: $ P(5) = 250 \times 2^{5} = 250 \times 32 = 8000 $ bacteria.

So, there will be 8000 bacteria after 5 hours.

Eva Abramson · Answer

Assuming uniform exponential growth, the population doubles every 8 hours. We can write the formula for the population as

#p(t) = 250*2^(t/8)# where #t# is measured in hours.

5 hours after the starting point, the population will be

#p(5) = 250*2^(5/8) ~= 386#