Question

The bacteria in a certain culture triples every 7.7 hours. The culture has 6,500 bacteria at the start. How many bacteria will the culture contain after 4 hours?

Answer 1

11505 bacteria

Explanation:

Given :

The bacteria in a certain culture triples every 7.7 hours. The culture has 6,500 bacteria at the start .

As per the exponential growth , we have
`A=P_0\left ( R \right )^{(T)/(P)}`

Here ,

`P_0` is starting number of bacteria

R is rate at which number of bacteria increases

T is time elapsed

P is one period of rate

`P_0 = 6500\\R=3\\T=4\\P=7.7`

On putting these values in formula
`A=P_0\left ( R \right )^{(T)/(P)}` , we get

`A=P_0\left ( R \right )^{(T)/(P)}\\=6500\left ( 3 \right )^{(4)/(7.7)}\\ \approx 6500\left ( 3 \right )^(0.5195)\\=6500* 1.77\\=11505`

So, the culture will contain 11505 bacteria after four hours .