Question

The last 8 individuals of a critically endangered Hawaiian honeycreeper were brought into captivity in 2003. By 2022,

the captive population grew to 494 birds.
A. ~ 0.84
B. ~ 2.24
C. ~ 1.24
D. ~ 1.14

can you show how you got to that answer

Answer 1

The average annual rate of increase of the Hawaiian honeycreeper population from 2003 to 2022 is calculated using the compound annual growth rate (CAGR) formula. It comes out to be approximately 1.24 or a 24% increase per year.

The correct option C.

Step-by-step explanation:

To determine the average annual rate of increase of the Hawaiian honeycreeper population from 8 to 494 birds, we'll use the formula for compound annual growth rate (CAGR), which is CAGR = (EV/BV)^(1/n) - 1, where EV is the ending value, BV is the beginning value, and n is the number of periods (years in this case).

Using the given numbers: EV = 494 birds, BV = 8 birds, and n = 2022 - 2003 = 19 years.

So, CAGR = (494/8)^(1/19) - 1.

First, calculate the growth factor: (494/8) = 61.75.

Second, calculate the 19th root of 61.75, which is approximately 1.24.

Finally, subtract 1 from 1.24 to get the rate: 0.24, or 24%.

The closest answer to 0.24 is option C, which is approximately 1.24.