a populatioin of bacteria has an initial size of 500. the population doubles every 7 hours.
a) how many bacteria will there be after 10 hours
b) when will there be 3000 bacter?
I keep getting answers that just don't make sense. Can someone do these out for me......its practice, not homework. I have a test tomorrow.
I would set my equation as
N = 500(2)^(t/7) , where 7 is the number of hours
a)when t=10
N = 500(2)^(10/7) = 1345.9 or 1346 bacteria
b) set 3000 = 500(2)^(t/7)
6 = 2^(t/7)
t/7 = log6/log2
t = 7log6/log2 = 18.1
makes sense ....
after 7 hours 1000
after 14 hours 2000
after 21 hours 4000 , 3000 seems reasonable after 18
sorry I forgot to mention I have to use the equation: p(t)= ce^kt
ok, then change it to
N = 500(e)^(kt)
when t = 7
1000 = 500(e)^(7k)
2 = (e)^(7k)
7k = ln2
k = ln2/7 = .09902
N = 500(e)^(.09902t)
now follow the same steps as before
a) let t=10 .... ( I got exactly the same answer as before)
Sure! I'll be happy to explain the steps to solve these problems.
a) To find the number of bacteria after 10 hours, given that the population doubles every 7 hours, we can break it down into two steps.
Step 1: Calculate the number of doublings that occur in 10 hours.
The number of doublings can be found by dividing the total time (10 hours) by the doubling time (7 hours):
Number of doublings = 10 hours / 7 hours = 1.43
Note: Since we cannot have a fraction of a doubling, we usually round this down to the nearest whole number, which means there will be one full doubling.
Step 2: Calculate the final number of bacteria after doubling the initial population.
To do this, we multiply the initial size by 2 for each doubling. Since there is one doubling (as calculated in step 1), we simply multiply the initial size by 2:
Final number of bacteria = Initial size × 2 = 500 × 2 = 1000 bacteria
Therefore, after 10 hours, there will be 1000 bacteria.
b) To determine when there will be 3000 bacteria, we need to find the number of doublings required.
Step 1: Calculate the number of doublings needed to reach 3000 bacteria.
We divide the target number (3000 bacteria) by the initial size (500 bacteria) to find the factor of increase:
Factor of increase = Target number / Initial size = 3000 bacteria / 500 bacteria = 6
Note: The factor of increase represents the number of times the population needs to double.
Step 2: Calculate the time required for that number of doublings.
We multiply the doubling time (7 hours) by the number of doublings needed (6):
Time required = Doubling time × Number of doublings = 7 hours × 6 = 42 hours
Therefore, it will take 42 hours for the population to reach 3000 bacteria.
Keep in mind that these calculations assume continuous exponential growth without any limiting factors. In real-world scenarios, population growth may be affected by various factors.