Answer:
11505 bacteria
Step-by-step 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 )^{\frac{T}{P}}](https://tex.z-dn.net/?f=A%3DP_0%5Cleft%20%28%20R%20%5Cright%20%29%5E%7B%5Cfrac%7BT%7D%7BP%7D%7D)
Here ,
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](https://tex.z-dn.net/?f=P_0%20%3D%206500%5C%5CR%3D3%5C%5CT%3D4%5C%5CP%3D7.7)
On putting these values in formula
, we get
![A=P_0\left ( R \right )^{\frac{T}{P}}\\=6500\left ( 3 \right )^{\frac{4}{7.7}}\\ \approx 6500\left ( 3 \right )^{0.5195}\\=6500\times 1.77\\=11505](https://tex.z-dn.net/?f=A%3DP_0%5Cleft%20%28%20R%20%5Cright%20%29%5E%7B%5Cfrac%7BT%7D%7BP%7D%7D%5C%5C%3D6500%5Cleft%20%28%203%20%5Cright%20%29%5E%7B%5Cfrac%7B4%7D%7B7.7%7D%7D%5C%5C%20%5Capprox%206500%5Cleft%20%28%203%20%5Cright%20%29%5E%7B0.5195%7D%5C%5C%3D6500%5Ctimes%201.77%5C%5C%3D11505)
So, the culture will contain 11505 bacteria after four hours .
Step-by-step explanation:
step 1: add the ratios
1/2 + 1/4 + 1/5 = 0.95
step 2: divide each ratio by the total sum of the ratios and multiply by a 100
(1/2 ÷ 0.95) × 100 = 52.63 rounded off equals to 53
(1/4 ÷ 0.95) × 100 = 26.31 rounded off equals to 26
(1/5 ÷ 0.95) × 100 = 21.05 rounded off equals to 21
These ratios should add up to a 100
so the ratio are 53 : 26 : 21