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Home » Solution:** To find the rate of change of \( V(t) - Get link 4share

Solution:** To find the rate of change of \( V(t) - Get link 4share

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question: How many numbers are in the list $ 2, 5, 8, \ldots, 32 $?

📌 Solution: The sequence increases by 3 each time. The nth term is $2 + (n-1) \times 3 = 3n - 1$. Set $3n - 1 = 32$: $3n = 33$, so $n = 11$. $\boxed{11}$### Question 1

📌 A scientist is studying the population growth of a species of bacteria. The population doubles every 3 hours. If the initial population is 500 bacteria, how many bacteria will there be after 24 hours?

📌 Determine the number of doubling periods in 24 hours:

📌 \( \frac{24 \text{ hours}}{3 \text{ hours/doubling period}} = 8 \text{ doubling periods} \).

📌 Calculate the final population using the formula for exponential growth:

📌 \( \text{Final population} = 500 \times 2^8 \).

📌 Calculate \( 2^8 = 256 \).

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