a culture started with 6,000 bacteria after 6 hours it grew to 7,200 bacteria predict how much it will grow in 17 hours

Answer:[tex]P(t) = 10058\ bacterias[/tex]Step-by-step explanation:To perform this calculation we must use the exponential growth formulaThe exponential growth formula is[tex]P(t) = Ae^{kt}[/tex]WhereA is the main coefficient and represents the initial population of bacteriae is the basek is the growth ratet is time in hours.Let's call t = 0 to the initial hour.At t = 0 the population of bacteria was 6000Therefore we know that:[tex]P(0) = 6000[/tex] bacteriaAfter t = 6 hours, the population of bacteria was 7200Then [tex]P(6) = 7200[/tex] .Now we use this data to find the variables a, and k.[tex]P(0) = 6000 =Ae ^{k(0)}\\\\6000 = A(e ^ 0)\\\\A = 6000[/tex].Then:[tex]P(6) = 6000e^{k(6)}\\\\7200 = 6000e ^{6k}\\\\\frac{7200}{6000} = e^{6k}\\\\ln(\frac{7200}{6000}) = 6k\\\\k = \frac{ln(\frac{7200}{6000})}{6}\\\\k =0.03039[/tex]Finally the function is:[tex]P(t) = 6000e^{0.03039t}[/tex]After 17 hours:[tex]t = 17 hours[/tex]So the population of bacteria after t=17 hours is:[tex]P(t) = 6000e^{0.03039(17)}[/tex][tex]P(t) = 10058\ bacterias[/tex]