how do you compare the approximate rate of change of the function over the interval 250 < p < 500 with that…

how do you compare the approximate rate of change of the function over the interval 250 < p < 500 with that of the interval 500 < p < 1000? what do these rates of change mean in the context of the problem? which of the statements below support the answers to the questions above? select all that apply. the rate of change over the interval 250 < p < 500 was 1/250. the rate of change over the interval 250 < p < 500 was less than the rate of change over the interval 500 < p < 1000. the rate of change over the interval 500 < p < 1000 was 1/500. it took the population 10 years (1 decade) to grow by 1/250,000 people from 250,000 to 500,000 people. the rate of change over the interval 250 < p < 500 and that over the interval 500 < p < 1000 were equal. the rate of change over the interval 250 < p < 500 was 250. the rate of change over the interval 500 < p < 1000 was 500. it took the population 10 years (1 decade) to grow by 250,000 people from 250,000 to 500,000 people. it took the population 10 years (1 decade) to grow by 500,000 people from 500,000 to 1,000,000 people. the rate of change over the interval 250 < p < 500 was greater than the rate of change over the interval 500 < p < 1000. it took the population 10 years (1 decade) to grow by 1/500,000 people from 500,000 to 1,000,000 people.

how do you compare the approximate rate of change of the function over the interval 250 < p < 500 with that of the interval 500 < p < 1000? what do these rates of change mean in the context of the problem? which of the statements below support the answers to the questions above? select all that apply. the rate of change over the interval 250 < p < 500 was 1/250. the rate of change over the interval 250 < p < 500 was less than the rate of change over the interval 500 < p < 1000. the rate of change over the interval 500 < p < 1000 was 1/500. it took the population 10 years (1 decade) to grow by 1/250,000 people from 250,000 to 500,000 people. the rate of change over the interval 250 < p < 500 and that over the interval 500 < p < 1000 were equal. the rate of change over the interval 250 < p < 500 was 250. the rate of change over the interval 500 < p < 1000 was 500. it took the population 10 years (1 decade) to grow by 250,000 people from 250,000 to 500,000 people. it took the population 10 years (1 decade) to grow by 500,000 people from 500,000 to 1,000,000 people. the rate of change over the interval 250 < p < 500 was greater than the rate of change over the interval 500 < p < 1000. it took the population 10 years (1 decade) to grow by 1/500,000 people from 500,000 to 1,000,000 people.

Answer

Explanation:

Step1: Recall rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, assume $P$ is the independent variable. But since we are not given the function, we work with the information about the intervals and the statements.

Step2: Analyze each statement

  1. For the statement "The rate of change over the interval $250<P<500$ was $\frac{1}{250}$": Without knowing the function, we can't confirm this value as the rate of change.
  2. For the statement "The rate of change over the interval $250<P<500$ was less than the rate of change over the interval $500<P<1000$": We need to calculate the rates of change for both intervals using the formula $\frac{\Delta y}{\Delta x}$. But again, without the function, we can't directly compare in this way.
  3. For the statement "The rate of change over the interval $500<P<1000$ was $\frac{1}{500}$": Without the function, we can't confirm this value.
  4. For the statement "It took the population 10 years (1 decade) to grow by $\frac{1}{250000}$ people from 250000 to 500000 people": This is an incorrect way of stating growth as $\frac{1}{250000}$ people is not a valid measure of population growth in this context.
  5. For the statement "The rate of change over the interval $250<P<500$ and that over the interval $500<P<1000$ were equal": Without calculating the rates of change, we can't say this.
  6. For the statement "The rate of change over the interval $250<P<500$ was 250": Without the function, we can't confirm this.
  7. For the statement "The rate of change over the interval $500<P<1000$ was 500": Without the function, we can't confirm this.
  8. For the statement "It took the population 10 years (1 decade) to grow by 250000 people from 250000 to 500000 people": This is a correct statement about the population - growth amount over the given interval.
  9. For the statement "It took the population 10 years (1 decade) to grow by 500000 people from 500000 to 1000000 people": This is a correct statement about the population - growth amount over the given interval.
  10. For the statement "The rate of change over the interval $250<P<500$ was greater than the rate of change over the interval $500<P<1000$": Without calculating the rates of change, we can't say this.
  11. For the statement "It took the population 10 years (1 decade) to grow by $\frac{1}{500000}$ people from 500000 to 1000000 people": This is an incorrect way of stating growth.

Answer:

It took the population 10 years (1 decade) to grow by 250000 people from 250000 to 500000 people. It took the population 10 years (1 decade) to grow by 500000 people from 500000 to 1000000 people.