Answer:
22.4 hours
Step-by-step explanation:
The population of bacteria is modelled by the equation:
[tex]P=P_0e^{rt}[/tex]
From the the question, the initial population of bacteria is 720.
So after 26 hours, we have:
[tex]P=2P_0[/tex]
This implies that:
[tex]2P_0=P_0e^{26r}[/tex]
[tex]2=e^{26r}[/tex]
[tex]26r = ln(2) [/tex]
[tex]r = \frac{ ln(2) }{26} [/tex]
[tex]r = 0.0267[/tex]
We want to find how long it will take for there to be 1310 bacteria present.
[tex]1310=720e^{0.0267t}[/tex]
[tex] \frac{1310}{720} = {e}^{0.0267t} [/tex]
[tex] \ln(\frac{1310}{720}) = {0.0267t} [/tex]
[tex]0.59853= {0.0267t} \\ t = \frac{0.59853}{0.0267} [/tex]
[tex]t = 22.417[/tex]
To the nearest tenth , it will take 22.4 hours
