The number of bacteria in a culture grows according to the formula [math]N(t)=N_0\cdot e^{0.05t}[/math], where t is the time in hours, and [math]N_0[/math] is the initial number of bacteria.
If there are initially 500 bacteria, how many bacteria will there be in the culture after 10 hours?
[math]N\left(10\right)=500\cdot e^{0.5}[/math][br][math]N\left(10\right)=500\sqrt{e}\simeq824[/math]
After how many hours will the initial number of bacteria double? [i](Round your answer to one decimal place).[/i]
[math]N\left(t\right)=100\Rightarrow e^{0.05t}=2\Rightarrow0.05t=ln2\Rightarrow t=20ln2....[/math][br][math]ln2\simeq0.693[/math]
In the GeoGebra window, interpret the equation N(t)=1000 graphically:[br]-draw the equation line y=1000[br]-find the intersection point of the two graphs[br]-check the solution found by calculation