Question

how many mold spores would there be after 10 days? How many spores were there two days prior to you finding the bread?

Answer 1

`\begin{gathered} P=208.926\cdot10^6\text{ spores after 10 days.} \\ P=3094.85\text{ spores after 2 days} \end{gathered}`

Explanation:

We can models this situation by using exponential growth, which is represented by the following formula:

`\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}`

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.

`\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}`

Now, after 2 days:

`\begin{gathered} P=192\cdot e^(1.39(2)) \\ P=3094.85\text{ spores after 2 days} \end{gathered}`