Respuesta :
The given information is:
The starting population of bacteria is 390.
The population quadruples every 20 minutes.
To find the equation of the population in terms of minutes, we can apply the following formula:
[tex]P(t)=P_0\cdot4^{(\frac{t}{20})}[/tex]Where P0 is the starting population, the number 4 is because the population quadruples every 20 minutes (the 20 in the power is given by this), it is equal to 4 times the initial number, and t is the time in minutes.
If we replace the known values, we obtain:
[tex]P(t)=390\cdot4^{(\frac{t}{20})}[/tex]To find the population after 1 hour, we need to convert 1 hour to minutes, and it is equal to 60 minutes, then we need to replace t=60 in the formula and solve:
[tex]\begin{gathered} P(60)=390\cdot4^{(\frac{60}{20})} \\ P(60)=390\cdot4^3 \\ P(60)=390\cdot64 \\ P(60)=24960\text{ bacterias} \end{gathered}[/tex]Thus, after 1 hour there are 24960 bacterias.
