Question 46 istitutional Correlates.Science 194,368581pp. 732–734.385609360557346433a. Plot the log of brain size against the log bodyweight.b. Find the best-fitting line using least squaresregression on the log-transformed data.44. Rivers and streams carry small solid particles ofrock and mineral downhill, either suspended inthe water column (“suspended load") or bounced,rolled, or slid along the river bed (“bed load").Solid particles are classified according to theirmean diameter from smallest to largest as clay,silt, sand, pebble, cobble, and boulder. Duringlow velocity flow, only very small particles (clayand silt) can be transported by the river, whereasduring high velocity flow, much larger particlesmay be transported, as documented in the tablebelow.438840392623324387360479413754276235387538345438395584Data source: Johnson, A. Resultsfrom Analyzing Metals in 1999Spokane River Fish and CrayfishSamples (Washington State Dept.of Ecology report, 2000).a. Plot the log of weight against length.b. Find the best-fitting line using least squaresregression on the transformed data.46. Consider the first four entries presented in the tablebelow, which represent one estimate of the world'spopulation levels over the second millennium AD:Diameter ofSpeed ofobjectsmoved (mm)currentClassification(m/sec)of objects0.20.10MudPopulationsize x (in billions)1.30.25SandYear AD (t)0.50Gravel110.75Coarse gravel10000.31201.00Pebbles12500.40451.50Small stones15000.50802.50Large stones (fist sized)17500.791803.50BouldersData soure: Nielsen A. (1950). “The Torrential InvertebrateFauna," Oikos 2: 176–196.Provide a semi-log plot of the points (t, In x) and findand graph the best-fitting line through these points 1.7 Sequences and Difference Equations 85on the same plot. From this line, provide an estimateof the average growth rate exponent r for the pop-ulation size function x(t) = ce"' over this period of750 years.48. Consider the entries presented in the table below,which represent one estimate of the world's popula-tion levels over the period 1920 to 2010:Populationsize x (in billions)47. Consider the entries presented in the table below,which represent one estimate of the world's popula-tion levels over the period 1750 to 1920:Year AD (t)19201.8619302.07Populationsize x (in billions)19402.30Year AD (t)19502.5219603.0217500.7919703.7018000.9819804.4418501.2619905.2719001.6519995.9819101.7520106.8619201.86Provide a semi-log plot of the points (t, In x) and findand graph the best-fitting line through these pointson the same plot. From this line, provide an estimateof the average growth rate exponent r for the pop-ulation size function x(t) = ce'' over this 170-yearperiod.Provide a semi-log plot of the points (t, In x) and findand graph the best-fitting line through these pointson the same plot. From this line, provide an estimateof the average growth rate exponent r for the pop-ulation size function x(t) = ce"' over this 90-yearperiod.1.7Sequences and Difference EquationsOften, experimental measurements are collected at discrete intervals of time. For ex-ample, the number of elephants in wildlife park in Africa may be counted every yearto ensure that poachers are not exterminating the population. Blood may be drawnon a weekly basis from a patient infected with HIV and the number of CD4+ cellsproduced by the patient's immune system counted to monitor patient response to

Question

Question 46 istitutional Correlates.Science 194,368581pp. 732–734.385609360557346433a. Plot the log of brain size against the log bodyweight.b. Find the best-fitting line using least squaresregression on the log-transformed data.44. Rivers and streams carry small solid particles ofrock and mineral downhill, either suspended inthe water column (“suspended load&#34;) or bounced,rolled, or slid along the river bed (“bed load&#34;).Solid particles are classified according to theirmean diameter from smallest to largest as clay,silt, sand, pebble, cobble, and boulder. Duringlow velocity flow, only very small particles (clayand silt) can be transported by the river, whereasduring high velocity flow, much larger particlesmay be transported, as documented in the tablebelow.438840392623324387360479413754276235387538345438395584Data source: Johnson, A. Resultsfrom Analyzing Metals in 1999Spokane River Fish and CrayfishSamples (Washington State Dept.of Ecology report, 2000).a. Plot the log of weight against length.b. Find the best-fitting line using least squaresregression on the transformed data.46. Consider the first four entries presented in the tablebelow, which represent one estimate of the world'spopulation levels over the second millennium AD:Diameter ofSpeed ofobjectsmoved (mm)currentClassification(m/sec)of objects0.20.10MudPopulationsize x (in billions)1.30.25SandYear AD (t)0.50Gravel110.75Coarse gravel10000.31201.00Pebbles12500.40451.50Small stones15000.50802.50Large stones (fist sized)17500.791803.50BouldersData soure: Nielsen A. (1950). “The Torrential InvertebrateFauna,&#34; Oikos 2: 176–196.Provide a semi-log plot of the points (t, In x) and findand graph the best-fitting line through these points 1.7 Sequences and Difference Equations 85on the same plot. From this line, provide an estimateof the average growth rate exponent r for the pop-ulation size function x(t) = ce&#34;' over this period of750 years.48. Consider the entries presented in the table below,which represent one estimate of the world's popula-tion levels over the period 1920 to 2010:Populationsize x (in billions)47. Consider the entries presented in the table below,which represent one estimate of the world's popula-tion levels over the period 1750 to 1920:Year AD (t)19201.8619302.07Populationsize x (in billions)19402.30Year AD (t)19502.5219603.0217500.7919703.7018000.9819804.4418501.2619905.2719001.6519995.9819101.7520106.8619201.86Provide a semi-log plot of the points (t, In x) and findand graph the best-fitting line through these pointson the same plot. From this line, provide an estimateof the average growth rate exponent r for the pop-ulation size function x(t) = ce'' over this 170-yearperiod.Provide a semi-log plot of the points (t, In x) and findand graph the best-fitting line through these pointson the same plot. From this line, provide an estimateof the average growth rate exponent r for the pop-ulation size function x(t) = ce&#34;' over this 90-yearperiod.1.7Sequences and Difference EquationsOften, experimental measurements are collected at discrete intervals of time. For ex-ample, the number of elephants in wildlife park in Africa may be counted every yearto ensure that poachers are not exterminating the population. Blood may be drawnon a weekly basis from a patient infected with HIV and the number of CD4+ cellsproduced by the patient's immune system counted to monitor patient response to

Accepted Answer

46.
From the given information,

t
x

1000
0.31

1250
0.4

1500
0.5

1750
0.79

Consider,…