Experts fear that without conservation efforts, an endangered species could disappear from the wild by 2022. Just one hundred years ago, there were at least 100,000 of this endangered species. By 2010, the estimated world population of this endangered species was 5000. The bar graph shows the estimated world population of this endangered species for selected years from 1970 through 2010. Also shown is a polynomial function, with its graph, that models the data. Use this information to complete parts a through c.

Question

Experts fear that without conservation​ efforts, an endangered species could disappear from the wild by 2022. Just one hundred years​ ago, there were at least​ 100,000 of this endangered species. By​ 2010, the estimated world population of this endangered species was 5000. The bar graph shows the estimated world population of this endangered species for selected years from 1970 through 2010. Also shown is a polynomial​ function, with its​ graph, that models the data. Use this information to complete parts a through c. 
LOADING... Click the icon to view the bar graph and the graph of the polynomial function. 
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Part 1
a. Find and interpret​ f(40). 
In the year 
▼ 
2010
1980
2020
40
1990
2000
​, the polynomial estimates the population of this species to be 
  
enter your response here.
​(Round to the nearest integer as​ needed.)

GPT-4o mini · Answer

To answer question a, we first need to determine what \( f(40) \) represents. Given that the context is a model for the population of an endangered species from 1970 through 2010, and the year 1970 corresponds to \( t = 0 \), we can deduce that \( t = 40 \) corresponds to the year \( 1970 + 40 = 2010 \).

To find \( f(40) \), we would typically refer to the polynomial function that models the population and evaluate it at \( t = 40 \). Since the actual polynomial function and the bar graph are not provided here, I will guide you on how to interpret \( f(40) \) in a standard context.

Find \( f(40) \): Plug \( t = 40 \) into the polynomial function. If the polynomial is given explicitly, substitute \( t \) with 40 and calculate.
Interpret the result: The output of \( f(40) \) represents the estimated population of the endangered species in the year 2010.
Round to the nearest integer: If your result is not an integer, you would round it to the nearest whole number.

After calculating \( f(40) \) with the polynomial function:

If \( f(40) \approx 5000 \), you would state: "In the year 2010, the polynomial estimates the population of this species to be approximately 5000."

Make sure to use the exact model provided to you for the most accurate response.