the graph given below shows the population ( p ) in a small industrial city from 1970 to 2020. the variable…

the graph given below shows the population ( p ) in a small industrial city from 1970 to 2020. the variable ( x ) represents the number of years since 1970.\n(a) what was the average rate of change of ( p ) between ( x = 0 ) and ( x = 20 )?\n(b) interpret the value of the average rate of change that you found in part (a).\n- the population did not experience any change during that time span.\n- the population decreased during that time span.\n- the population increased and decreased the same amount during that time span.\n- the population increased during that time span.\n(c) identify a time period where the average rate of change is 0.\n- ( 1990 - 2010 )\n- ( 1990 - 2020 )\n- ( 1995 - 2010 )\n- ( 1995 - 2020 )\n- ( 2010 - 2020 )

the graph given below shows the population ( p ) in a small industrial city from 1970 to 2020. the variable ( x ) represents the number of years since 1970.\n(a) what was the average rate of change of ( p ) between ( x = 0 ) and ( x = 20 )?\n(b) interpret the value of the average rate of change that you found in part (a).\n- the population did not experience any change during that time span.\n- the population decreased during that time span.\n- the population increased and decreased the same amount during that time span.\n- the population increased during that time span.\n(c) identify a time period where the average rate of change is 0.\n- ( 1990 - 2010 )\n- ( 1990 - 2020 )\n- ( 1995 - 2010 )\n- ( 1995 - 2020 )\n- ( 2010 - 2020 )

Answer

Explanation:

Step1: Recall the average 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, (a = 0), (b=20), (f(0)=30) (since when (x = 0), (P = 30) thousands) and (f(20)=50) (since when (x = 20), (P = 50) thousands).

Step2: Calculate the average rate of change

Substitute the values into the formula: (\frac{50 - 30}{20-0}=\frac{20}{20}=1).

Answer:

(a) (1) (thousand per year) (b) The population increased during that time span. (c) (1990 - 2010) (because if we assume (x = 20) corresponds to (1990) ((1970+20)) and (x = 40) corresponds to (2010) ((1970 + 40)), and if the population (P) is the same at (x = 20) and (x = 40) (from the graph's general shape, the average rate of change (\frac{f(40)-f(20)}{40 - 20}=0) when (f(40)=f(20)))