Question

The researcher decided that the population growth followed a geometric sequence. He wrote the explicit formula (a_n = 1000 cdot 2^n-1) to model the growth, and used this formula to predict the populations for years 6, 10, and 50. Do you agree with the researcher's method of predicting the populations? Why or why not?

a) Yes, because the formula accounts for exponential growth accurately.

b) No, because geometric sequences are not suitable for population growth predictions.

c) Yes, because the researcher considered the initial population.

d) No, because the formula does not involve the growth rate.

Answer 1

No, I do not agree with the researcher's method of predicting the populations using a geometric sequence formula because it does not take into consideration the restrictions and limitations that occur in real-life populations.

Step-by-step explanation:

No, I do not agree with the researcher's method of predicting the populations using a geometric sequence formula. While the formula accurately accounts for exponential growth, it does not take into consideration the restrictions and limitations that occur in real-life populations. In reality, population growth is more accurately modeled by the logistic growth model, which introduces limits to reproductive growth as the population size increases.

In the logistic growth model, the population starts out growing exponentially, but as the population size increases, the growth rate slows down and eventually levels off to zero. This is more representative of what happens in natural populations when resources become limited and competition for resources increases. Therefore, the use of a geometric sequence formula is not suitable for predicting population growth in real-life scenarios.