If we assume the population of Grand Rapids is growing at a rate of approximately 4% per decade, we can model the population function with the formula P( t ) = 181843 ( 1.04 )^(t / 10). Use this formula to compute the average rate of change of the population on the intervals [ 5 , 10 ] , [ 5 , 9 ] , [ 5 , 8 ] , [ 5 , 7 ] , and [ 5 , 6 ] .

Answer:The average rate of change of the population on the intervals [ 5 , 10 ] , [ 5 , 9 ] , [ 5 , 8 ] , [ 5 , 7 ] , and [ 5 , 6 ]  are 734.504, 733.06, 731.62, 730.185 and 728.75 respectively.Step-by-step explanation:The given function is[tex]P(t)=181843(1.04)^{(\frac{t}{10})}[/tex]where, P(t) is population after t years.At t=5,[tex]P(5)=181843(1.04)^{(\frac{5}{10})}=185444.20[/tex]At t=6,[tex]P(6)=181843(1.04)^{(\frac{6}{10})}=186172.95[/tex]At t=7,[tex]P(7)=181843(1.04)^{(\frac{7}{10})}=186904.57[/tex]At t=8,[tex]P(8)=181843(1.04)^{(\frac{8}{10})}=187639.06[/tex]At t=9,[tex]P(9)=181843(1.04)^{(\frac{9}{10})}=188376.44[/tex]At t=10,[tex]P(10)=181843(1.04)^{(\frac{10}{10})}=189116.72[/tex]The rate of change of P(t) on the interval [tex][x_1,x_2][/tex] is [tex]m=\frac{P(x_2)-P(x_1)}{x_2-x_1}[/tex]Using the above formula, the average rate of change of the population on the intervals [ 5 , 10 ] is[tex]m=\frac{P(10)-P(5)}{10-5}=\frac{189116.72-185444.20}{5}=734.504[/tex]The average rate of change of the population on the intervals [ 5 , 9 ] is[tex]m=\frac{P(9)-P(5)}{9-5}=\frac{188376.44-185444.20}{4}=733.06[/tex]The average rate of change of the population on the intervals [ 5 , 8 ] is[tex]m=\frac{P(8)-P(5)}{8-5}=\frac{187639.06-185444.20}{3}=731.62[/tex]The average rate of change of the population on the intervals [ 5 , 7 ] is[tex]m=\frac{P(7)-P(5)}{7-5}=\frac{186904.57-185444.20}{2}=730.185[/tex]The average rate of change of the population on the intervals [ 5 , 6 ] is[tex]m=\frac{P(6)-P(5)}{6-5}=\frac{186172.95-185444.20}{1}=728.75[/tex]Therefore the average rate of change of the population on the intervals [ 5 , 10 ] , [ 5 , 9 ] , [ 5 , 8 ] , [ 5 , 7 ] , and [ 5 , 6 ]  are 734.504, 733.06, 731.62, 730.185 and 728.75 respectively.