A bacteria culture initially contains 2000 bacteria and doubles every half hour.

Question

Please help me find out what is the size of bacterial population after 5 hours

A bacteria culture initially contains 2000 bacteria and doubles every half hour. Find the size of the baterial population after 20 minutes. 3175 Find the size of the baterial population after 5 hours.

Answer 1

Hi Ashley,

For this problem, we are going to be using an exponential model because the bacteria culture is doubling every 30 minutes.

f(x) = a(b^x)

where a = initial amount

b = rate of growth

x = the number of minutes/hours

We know that we initially have 2000 bacterias which means that 2000 will be our "a" value.

Doubling would indicate that 2 will be our "b" value

In this case, let's assume that x moves in increments of 60 minutes/1 hours. If doubling is happening every half and hour, that means that the exponent will be 2x.

So now let's rewrite this equation to reflect the values in the problem

f(x) = 2000(2^(2x)

Let's substitute 5 for x to find the number of bacteria after 5 hours.

f(5) = 2000(2^(2(5))

f(5) = 2000(2^10)

f(5) = 2000(1024)

f(5) = 2048000

Hope that helps!

Answer 2

A(5) = 2000(2)^(5)/(0.5) , 30 minutes is 0.5 hours