Respuesta :
Answer:
The function that can be used to describe the number (n) of bacteria after 2 minutes is;
[tex]P = 4 \cdot e^{\left(\dfrac{ln(32)}{5} \times 2\right)} \approx 4 \cdot e^{\left(0.693\times 2\right)}[/tex]
Step-by-step explanation:
The data in the table are presented as follows;
Number of bacteria; 4, 128, 4,096, 131,072
Number of minutes from initial state; 0, 5, 10, 15
The general equation for population growth is presented as follows;
[tex]P = P_0 \cdot e^{r\cdot t}[/tex]
Where;
P = The population after 't' minutes
P₀ = The initial population
r = The population growth rate
t = The time taken for the growth in population numbers
At t = minutes. we have;
[tex]4 = P_0 \cdot e^{r\times0} = P_0[/tex]
∴ P₀ = 4
At t = 5, we have;
[tex]128 = 4 \cdot e^{r\times 5}[/tex]
[tex]\therefore e^{r\times 5} = \dfrac{128}{4} = 32[/tex]
[tex]ln\left(e^{r\times 5}\right) = ln(32)[/tex]
∴ r × 5 = ㏑(32)
r = ln(32)/5 ≈ 0.693
The number (n) of bacteria after 2 minutes is therefore;
[tex]P = 4 \cdot e^{\left(\dfrac{ln(32)}{5} \times 2\right)} \approx 4 \cdot e^{\left(0.693\times 2\right)}[/tex]
