Math / Calculus

QuestionSection C(One Questions) (15 Marks) Let the rate of increase of bacteria is proportional to its size it is found that a culture of 300 bacteria has increased to 6 hundrod affer 90 minutes. (a) Express the population after $t$ hours as a function of $f$ . (b) How many bacteria are there in 5 hours? (c) How many hours and minutes will it take the culture to reach 20,000 bacteria. ( 3 marks

Studdy Solution
Calculate $t$ : $t \approx \frac{1.5 \times 4.3219}{0.6931}$ $t \approx 9.35 \text{ hours}$ Convert 0.35 hours to minutes: $0.35 \times 60 \approx 21 \text{ minutes}$
The population after 5 hours is approximately 2400 bacteria, and it will take approximately 9 hours and 21 minutes for the culture to reach 20,000 bacteria.

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