Question

Emerald ash borers were accidentally introduced to Michigan from Asia in wooden shipping crates. They have since killed hundreds of millions of trees. The ash borer was first found in Boulder, Colorado in 2013. If the Colorado population started with 2 individuals in 2013, and its intrinsic rate of increase (r) is estimated to be 1.5, what is the population size estimated to be in 2025 (to within an order of magnitude)?

A. 36
B. 1.5x102
C. 1.3x108
D. 3.0x1012

The growth rate of the population described in Question 8 (regulated by intraspecific competition, carrying capacity of 500 individuals, intrinsic rate of increase of 0.7, current population size of 514 individuals) is actually affected by a time lag of 1 year. The previous year's population size was 480 individuals. Its growth rate should be:

A. - 10.1 individuals per unit time

B. - 0.028 individuals per unit time

C. 0.7 individuals per unit time

D. 14.4 individuals per unit time

Answer 1

The estimated population size of the emerald ash borer in 2025 falls within the range of 1.3x10^8 individuals. Therefore, the correct option is C.

The growth rate of the population affected by a time lag and regulated by intraspecific competition and carrying capacity is -10.1 individuals per unit time.Therefore, the correct option is A.

Step-by-step explanation:

The emerald ash borer's population can be estimated using the formula for exponential growth given its intrinsic rate of increase (r). If we assume it started with 2 individuals in 2013 and has r = 1.5, to estimate the population size in 2025, we would calculate it as follows:

P(t) = P0 * e^(rt)

Since t = 2025 - 2013 = 12 years, and P0 = 2,

P(12) = 2 * e^(1.5*12)

This calculation results in an estimate that falls within the range of option C, which is 1.3x10^8 individuals.

For the second question concerning the population affected by a time lag and regulated by intraspecific competition with a carrying capacity, we need to use logistic growth models with a time lag.

The growth rate can be computed considering the current and previous year's population sizes and the effect of carrying capacity:

Growth Rate = r * (1 - (Population(t-1)/Carrying Capacity)) * Population(t)

Using the given values: r = 0.7, Carrying Capacity = 500, Population(t-1) = 480, and Current Population = 514,

Growth Rate = 0.7 * (1 - (480/500)) * 514

The computed growth rate falls within the range of option A, which is -10.1 individuals per unit time, indicating a decline in the population size.