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You are tracking a prairie dog population that is growing geometrically. In the event that a prairie dog town has 30 residents in the first year and 33 in the following year. How many people are anticipated to live in the seventh year?

A. ~51 individuals.
B. ~64 individuals.
C. ~114 individuals.
D. ~58 individuals.

In 2003 the last eight members of a Hawaiian honeycreeper highly endangered species were transferred into captivity. Fourth ninety-four birds were in captivity by 2022.
A. ~ 0.84
B. ~ 2.24
C. ~ 1.24
D. ~ 1.14

1 Answer

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The people are anticipated to live in the seventh year D. ~58 individuals. Fourth ninety-four birds were in captivity by 2022 is D. ~ 1.14 .Therefore, D. ~58 individuals ,D. ~ 1.14 is correct .

The population is growing geometrically, which means that the population is multiplied by a constant factor each year.

The constant factor, also known as the growth rate, can be calculated as follows:

growth_rate = (33 - 30) / 30 = 0.1

This means that the population is increasing by 10% each year.

We can use the following formula to calculate the population after 7 years:

final_population = initial_population * (1 + growth_rate) ^ number_of_years

where:

initial_population is the population in the first year (30)

growth_rate is the growth rate per year (0.1)

number_of_years is the number of years (7)

Plugging in the values, we get:

final_population = 30 * (1 + 0.1) ^ 7 ≈ 58.2.

Given the information provided, it is not possible to determine the exact growth rate of the population each year.

However, we can estimate the average annual growth rate by assuming that the population grew exponentially.

The average annual growth rate can be calculated using the following formula:

average_annual_growth_rate = (final_population / initial_population) ^ (1 / years) - 1

where:

final_population is the population in 2022 (94)

initial_population is the population in 2003 (8)

years is the number of years between 2003 and 2022 (19)

Plugging these values into the formula, we get:

average_annual_growth_rate = (94 / 8) ^ (1 / 19) - 1 ≈ 0.014

This means that the average annual growth rate of the population was approximately 1.4%.

The doubling time of the population can be calculated using the following formula:

doubling_time = 70 / average_annual_growth_rate

where:

doubling_time is the number of years it takes for the population to double

average_annual_growth_rate is the average annual growth rate

Plugging in the average annual growth rate that we calculated earlier, we get:

doubling_time = 70 / 0.014 ≈ 505.56 years

This means that it takes approximately 505

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