Respuesta :
Answer:
The initial population was 2810
The bacterial population after 5 hours will be 92335548
Step-by-step explanation:
The bacterial population growth formula is:
[tex]P = P_0 \times e^{rt} [/tex]
where P is the population after time t, [tex]P_0[/tex] is the starting population, i.e. when t = 0, r is the rate of growth in % and t is time in hours
Data: The doubling period of a bacterial population is 20 minutes (1/3 hour). Replacing this information in the formula we get:
[tex]2 P_0 = P_0 \times e^{r 1/3} [/tex]
[tex]2 = e^{r \; 1/3} [/tex]
[tex]ln 2 = r \; 1/3 [/tex]
[tex]ln 2 \times 3 = r [/tex]
[tex]2.08 \% = r [/tex]
Data: At time t = 100 minutes (5/3 hours), the bacterial population was 90000. Replacing this information in the formula we get:
[tex]90000 = P_0 \times e^{2.08 \; 5/3} [/tex]
[tex]\frac{9000}{e^{2.08 \; 5/3}} = P_0 [/tex]
[tex]2810 = P_0 [/tex]
Data: the initial population got above and t = 5 hours. Replacing this information in the formula we get:
[tex]P = 2810 \times e^{2.08 \; 5} [/tex]
[tex]P = 92335548[/tex]
