Could someone please check my work and let me know if if it's correct

D H M E Consider the following data set. Year 1814 1824 1834 1844 1854 1864 Population 125 275 830 1200 1750 1650 a). First input the data in the above and Plot the data year versus population 2000 Year Population 1800 1814 125 1600 1824 275 Plot! 1400 1834 830 1200 1844 1200 1000 1854 1750 is this the carrying capacity? 800 1864 1650 starts to decrease here 600 400 carrying capacity is about 1755 200 1810 1820 1830 1840 1850 1860 1870 b). Is there a trend? Please select the right answer in the below. YES There is a trend of population increase from 1814 to 1854, then a small decrease in 1864. c). Plot the change in population versus years elapsed after 1814. change in population versus year X-axis observation y-axis Year Population p_(n+1) p n 600 1814 125 150 500 1824 275 555 400 1834 830 370 1844 1200 550 300 1854 1750 -100 200 1864 1650 100 1820 1825 1830 1835 -100 1840 1845 1850 1855 1860 1865 1870 -200 d). Formulate a discrete dynamical system that reasonably approximates the change you have observed. 6 ???? P (n+1)=p_n+b where b=some amount of population increase/decrease every decade P_0=125 p_n+1=population in next decade _n=current population observation prediction year Population p_(n+1)-p_n (1755-p_n)p_n k=[p_(n+1)-p_n]/[(1755-p_n)pin] _n+k(1755-p_n)p_n 1814 125 150 203750 0.000736196 125 1824 555 407000 0.001363636 use this for k=.0014 410.25 1834 830 370 767750 0.000481928 844.8 1844 1200 550 666000 0.000825826 1904.85 1854 1750 -100 8750 0.011428571 2132.4 1864 1650 1762.25 ???? dynamical system: p_(n+1)=p_n+.0014(1755-p_n)p_n where k=.0014 and carrying capacity=1755 0 0=125 p_n+1=population in next decade p_n=current population blue dots: year v.s population red dots: year v.s prediction 2500 2000 1500 Plot Area 1000 500 1810 1820 1830 1840 1850 1860 1870