# Question #b1d2e

Jan 21, 2017

$2 , 048 , 000$ bacteria

#### Explanation:

We can say straightaway that

$B \left(t\right) = {B}_{o} \cdot {2}^{\frac{t}{0.25}}$

To check this:

• To start with: $B \left(0\right) = {B}_{o} \cdot {2}^{0} = {B}_{o}$

• Then: $B \left(0.25\right) = {B}_{o} \cdot {2}^{\frac{0.25}{0.25}} = 2 {B}_{o}$ so it is doubling :)

• And: $B \left(0.50\right) = {B}_{o} \cdot {2}^{\frac{0.50}{0.25}} = 4 {B}_{o}$, so it has quadrupled. The pattern is established.

Now, if at time 1.25 hours, there are 40,000 bacteria present, we can say that:

$40 , 000 = {B}_{o} \cdot {2}^{\frac{1.25}{0.25}} = 5 {B}_{o} \implies {B}_{o} = 8 , 000$

So:

$\textcolor{b l u e}{B \left(t\right) = 8 , 000 {\left(2\right)}^{\frac{t}{0.25}}}$

After 2 hours:

$B \left(2\right) = 8 , 000 \cdot {2}^{\frac{2.00}{0.25}}$

$= 8 , 000 \cdot {2}^{8} = 2 , 048 , 000$