Respuesta :
EXPLANATION
Let's see the facts:
Period = 72 hours
Initial Population= 105,700
Time = 216 hours
The equation is as follows:
[tex]P=P_0e^{rt}^{}[/tex]P_0=Initial Population
r= rate of growth
t=time
First, we need to find r:
In 72 hours ------> 2*105,700 = 211,400 bacteria
Replacing terms:
[tex]211,400=105,700e^{(r72)}[/tex]Dividing both sides by 105,700:
[tex]\frac{211,400}{105,700}=e^{(72r)}[/tex]Applying ln to both sides:
[tex]\ln (\frac{211,400}{105,700})=\ln (e^{72r})[/tex]Simplifying:
[tex]\ln (\frac{211,400}{105,700})=72r\cdot\ln e[/tex]Dividing both sides by 72:
[tex]\frac{\ln (\frac{211,400}{105,700})}{72}=r[/tex]Switching sides:
[tex]r=\frac{\ln (\frac{2114}{1057})}{72}[/tex]Simplifying:
[tex]r=\frac{0.69}{72}=0.009627[/tex]Now that we have r=0.009627 we can calculate the value of P as shown as follows:
[tex]P=105,700e^{(0.009627\cdot216)}[/tex]Multiplying terms:
[tex]P=105,700\cdot e^{(2.08)}^{}[/tex]Now, we can solve the expression:
[tex]P=105,700\cdot8=845,600[/tex]The answer is 845,600 bacteria.
