Question

(PLZ NEED HELP) The doubling time of a bacterial population is 10 minutes. After 80 minutes, the bacterial population was 80000. _____
Using your rounded answer for the initial population above (do not round your growth rate), find the size of the bacterial population after 5 hours.____

Answer 1

Answer:

Initial population = 313

Population after 5 hours = $3.36 \times 10^{11}$

Step-by-step explanation:

Let initial population = $x$

It is given that population gets doubled every 10 minutes.

Population after 10 minutes = $2x$

Population after 20 minutes = $2^{2} x$

:

:

Population after 80 minutes = $2^{8} x$ and it is given as 80000.

$\Rightarrow 2^{8} x = 80000\\\Rightarrow x = \dfrac{80000}{256}\\\Rightarrow x = 313$

So, initial population is 312.5 = ~313

To find, population after 5 hours i.e. 5 $\times$ 60 = 300 minutes

Population after 300 minutes =

$2^{30} x\\\Rightarrow 2^{30} \times 313\\\Rightarrow 3.36 \times 10^{11}$

So, the answers are:

Initial population = 313

Population after 5 hours = $3.36 \times 10^{11}$