Answer:
[tex]\begin{gathered} P=208.926\cdot10^6\text{ spores after 10 days.} \\ P=3094.85\text{ spores after 2 days} \end{gathered}[/tex]
Step-by-step explanation:
We can models this situation by using exponential growth, which is represented by the following formula:
[tex]\begin{gathered} P=P_0\cdot e^{rt} \\ \text{where,} \\ P=\text{Total population after time t} \\ P_0=\text{ starting population} \\ r=\text{rate of growth} \\ t=\text{time} \\ \text{Euler's number} \end{gathered}[/tex]
Therefore, for a starting population of 192 mold spores, and since it quadrupled every day.
After 10 days:
If they quadruple every day, then P/P0=4 when t=1.
[tex]\begin{gathered} 4=e^{r(1)} \\ \text{Taking Ln on both sides:} \\ r=\ln (4)\approx1.39 \\ \text{After 10 days, substituting t=10} \\ P=192\cdot e^{1.39(10)} \\ P=208.926\cdot10^6\text{ spores after 10 days.} \end{gathered}[/tex]
Now, after 2 days:
[tex]\begin{gathered} P=192\cdot e^{1.39(2)} \\ P=3094.85\text{ spores after 2 days} \end{gathered}[/tex]
