Question

2) A population of 800 beetles is growing each month at a rate of 5%.

a) Write an equation that expresses the number of beetles at time x.
A) N(x) = 800(1 + 0.05)^x
B) N(x) = 800(0.05)^x
C) N(x) = 800 + 0.05x
D) N(x) = 800x + 5
b) About how many beetles will there be in 8 months?
A) Approximately 946 beetles
B) Approximately 889 beetles
C) Approximately 680 beetles
D) Approximately 760 beetles

Answer 1

The correct equation for the beetle population growth after x months is N(x) = 800(1 + 0.05)^x, and after 8 months, the beetle population would be approximately 1,188 beetles. The population is expected to follow an exponential growth pattern until resource limitations lead to a logistic growth pattern.

Step-by-step explanation:

The population of 800 beetles growing each month at a rate of 5% can be represented by an exponential growth model. The correct equation to express the number of beetles at time x months is A) N(x) = 800(1 + 0.05)^x. Exponential growth is characterized by a population size that increases at a greater and greater rate, where the growth rate is proportionate to the current population.

After 8 months, the beetle population can be calculated using this equation: N(8) = 800(1 + 0.05)^8. Plugging the values into the equation gives us approximately 1,188 beetles.

Based on the concept of exponential growth, we can expect the population of beetles to continue growing rapidly until it reaches a point where resources become limited, leading to a logistic growth pattern where the growth rate eventually slows down and levels off.