Answer :
After 24 hours, the cell count will be approximately 289.059 or rounded to 289 cells.
1. Initial population:The initial population is 100 cells.
2. Population growth after each hour:
- After each hour, the population increases by 3.5%. To find the population after each hour, we'll use the formula:
- [tex]\[ \text{Population after hour} = \text{Previous population} + (\text{Previous population} \times \text{Growth rate}) \][/tex]
3. Calculate the population after each hour:
- After the first hour: [tex]\[ \text{Population after 1st hour} = 100 + (100 \times 0.035) = 100 + 3.5 = 103.5 \][/tex]
- After the second hour:[tex]\[ \text{Population after 2nd hour} = 103.5 + (103.5 \times 0.035) = 103.5 + 3.6225 = 107.1225 \][/tex]
Continue this process for each hour up to 24 hours.
- After 24 hours, the population count will be:
- [tex]\[ \text{Population after 24 hours} = 100 \times (1 + 0.035)^{24} \][/tex]
- [tex]\[ \text{Population after 24 hours} = 100 \times (1.035)^{24} \][/tex]
- [tex]\[ \text{Population after 24 hours} \approx 100 \times 2.890591295 \][/tex]
- [tex]\[ \text{Population after 24 hours} \approx 289.0591295 \][/tex]
