Final answer:
The time it takes for the number of insects to reach at least 500 is calculated using the formula for exponential growth. After solving the equation, it's found that the time required is approximately 24 minutes, matching option (b).
Step-by-step explanation:
The question asks how long it will take for the number of insects, which quadruples every 8 minutes starting from 8, to reach at least 500. We can use the formula for exponential growth, which is P(t) = P0 * 4^(t/8), where P(t) is the population at time t, P0 is the initial population, and t is the time in minutes.
The initial population P0 is 8, and we want to find when the population reaches at least 500. Using the formula, we have 500 = 8 * 4^(t/8), which can be simplified to 62.5 = 4^(t/8). To solve for t, we can take the logarithm of both sides and get t/8 = log4(62.5). This gives us t = 8 * log4(62.5), and after calculating, we find that t is approximately 24 minutes, so the number of insects will reach at least 500 in about 24 minutes, which corresponds to option (b).