To determine how many bacteria there will be after 3 days given an initial count and a growth rate, we need to follow these steps:
1. Initial Conditions:
- Initial number of bacteria: [tex]\( 2.4 \)[/tex] million.
- Growth rate per hour: [tex]\( 4.3\% \)[/tex], which is [tex]\( 0.043 \)[/tex] in decimal form.
- Number of hours in a day: [tex]\( 24 \)[/tex].
- Number of days: [tex]\( 3 \)[/tex].
2. Total Time:
- Calculate the total number of hours over the 3 days:
[tex]\[
\text{Total hours} = 24 \, \text{hours/day} \times 3 \, \text{days} = 72 \, \text{hours}
\][/tex]
3. Growth Factor:
- The bacteria's growth rate is compounded each hour. The growth factor for one hour is [tex]\( 1 + 0.043 = 1.043 \)[/tex].
- Over the total period of 72 hours, the growth factor becomes:
[tex]\[
\text{Total growth rate} = (1.043)^{72}
\][/tex]
4. Calculate the Final Amount of Bacteria:
- Multiply the initial number of bacteria by the total growth rate:
[tex]\[
\text{Final amount of bacteria} = 2.4 \times (1.043)^{72}
\][/tex]
- This results in approximately [tex]\( 49.73721326128391 \)[/tex] million bacteria.
5. Rounding the Answer:
- To get the final answer rounded to the nearest tenth of a million:
[tex]\[
\text{Final amount rounded} = 49.7 \, \text{million}
\][/tex]
Thus, after 3 days, there will be approximately [tex]\( 49.7 \)[/tex] million bacteria.
