Answer: There is 3.994% continuous growth rate per hour.
Step-by-step explanation:
Since we have given that
Initial bacteria = 2600
After two and a half hours,
Number of bacteria = 2873
We need to find the continuous growth rate per hour.
As we know the equation for continuous growth rate per hour.
[tex]y=y_0e^{rt}\\\\2873=2600e^{2.5r}\\\\\dfrac{2873}{2600}=e^{2.5r}\\\\1.105=e^{2.5r}\\\\\text{Taking log on both the sides}\\\\\ln 1.105=2.5r\\\\0.0998=2.5r\\\\r=\dfac{0.0998}{2.5}\\\\r=0.0399\times 100\\\\r=3.994\%[/tex]
Hence, there is 3.994% continuous growth rate per hour.
