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Calculate the population of fruit flies at the end of 4 days if the population starts out at 24 flies per room and grows at a rate of 6.9?

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Final answer:

Using the exponential growth formula P = P_0 × r^n, the population of fruit flies after 4 days, starting from 24 flies and growing at a rate of 6.9, is approximately 54888 flies.

Step-by-step explanation:

To calculate the population of fruit flies at the end of 4 days given an initial population of 24 flies and a growth rate of 6.9, it is assumed that '6.9' refers to the daily multiplicative growth factor (i.e., the population multiplies by 6.9 each day). To find the population after 4 days, we can use the formula for exponential growth: P = P_0 × rⁿ, where P is the final population, P_0 is the initial population, r is the growth rate, and n is the number of time periods (days, in this case).

Starting with 24 flies, the population after one day would be 24 × 6.9. After two days, it would be (24 × 6.9) × 6.9, and so on. After four days, the population would be calculated as:

P = 24 × 6.9⁴

P = 24 × 2287.781

P = 54887.544 flies

Therefore, the population of fruit flies at the end of 4 days would be approximately 54887.544 or about 54888 flies when rounded to the nearest whole number.

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