Question

Suppose an experimental population of fruit flies increases according to the law of exponential growth. There were 100 flies after the second day of the experiment and 300 flies after the fourth day. Approximately how many flies were there in the original population?

Answer 1

The original population size of fruit flies in an exponential growth experiment, starting with 100 flies on the second day and 300 on the fourth day, is approximately 33 flies.

Step-by-step explanation:

The question asks us to approximate the original population of fruit flies based on a pattern of exponential growth. We have two data points: 100 flies on the second day and 300 flies on the fourth day. To find the initial population size, we will use the formula for exponential growth: N(t) = N0 * e^(kt), where N(t) is the population at time t, N0 is the initial population size, e is the base of the natural logarithm, and k is the growth rate.

We first need to find the rate of growth, k. We can set up two equations based on the data provided:

• 100 = N0 * e^(2k)
• 300 = N0 * e^(4k)

Dividing the second equation by the first gives us:

300 / 100 = (N0 * e^(4k)) / (N0 * e^(2k))

3 = e^(2k)

We can find k by taking the natural logarithm of both sides:

ln(3) = 2k

k = ln(3) / 2

Now, we substitute k back into one of our original equations to solve for N0:

100 = N0 * e^(ln(3) / 2 * 2)

100 = N0 * e^(ln(3))

100 = N0 * 3

N0 = 100 / 3

N0 ≈ 33.33

Therefore, the original population size was approximately 33 flies.