Baby growth curves!
The chart above depicts the theoretic optimal baby mass growth rate for my son, 6.5 ln(x)-11.3, and for a healthy Vietnamese baby, 5.6 ln(x)-9.8. The command to generate this plot for yourself is: plot 5.6 ln(x)-9.8,6.5 ln(x)-11.3 from x=9 to 44. The x-axis is the age of the baby in months post conception. Birth is at x = 9 months. The y-axis is the mass of the baby in kilograms.
__________ Calculate the birth mass of my son by evaluating his growth function at x = 9 months.
__________ Calculate the birth mass of a Vietnamese baby by evaluating their growth function at x = 9 months.
__________ Calculate the age of my son in months when his mass was equal to 10 kilograms.
__________ Based only on the graphs, will the Vietnamese baby ever have the same mass as my son?
__________ Calculate when my son's mass was equal to the Vietnamese babies mass by setting my son's growth equation equal to the Vietnamese baby's growth equation and have WolframAlpha solve for x.
Mathematical models!
The chart above depicts three possible models for a sprinter running the 100 meter dash. As listed in the chart legend from top to bottom, the models are exponential, logarithmic, and logistic. The command to generate this plot for yourself is: plot e^(0.025*x),2.6*ln(x),-12+24/(1+e^(-0.15*x)) from x=0 to 100.
The x-axis is the distance in meters from the starting line, the y-axis is the speed of the sprinter in meters per second.
___________________ Which of the three mathematical equations best models the distance verus speed for a sprinter?
_______ Using the best mathematical model for a sprinter, calculate the speed of the sprinter at a distance of ten meters.
_______ Using the best mathematical model for a sprinter, calculate the distance at which the sprinter has a speed of 6 m/s.
_______ Using the best mathematical model for a sprinter, calculate the highest speed that the sprinter attains during the 100 meter race.
The soil on Bikini atoll in the Marshall Islands is contaminated by the radioactive element Cesium-137. Like all radioactive elements, Cesium-137 will eventually decay into non-radioactive elements. The rate of decay is an exponential decay given by the formula N = P e− 0.023 t where P is the starting amount of Cesium in the soil in kilograms, t is the number of years, and N is the remaining amount of radioactive Cesium after that number of years.
__________ If there are 100 kilograms of Cesium-137 in the soil now, how many kilograms will be in the soil in 30 years?
____________ How many years until only one kilogram of the original 100 kilograms of Cesium-137 is left in the soil?
During a demonstration in physical science class on 09 June 2011, a marble was rolled from a height h on a ramp. The speed of the marble at the bottom of the ramp was measured. The data gathered is in the table below. Enter the following data into the LibreOffice.org Calc spreadsheet. Make an xy scattergraph. Determine the mathematical model that best fits for the data.
Height h (cm)
Velocity v (cm/s)
0
0
10
97
20
142
30
182
40
208
Write the mathematical model that best fits the data (round numbers to two decimal places):
__________ What will be the speed of the marble when the height h is 100 cm?
__________ From what height h will the marble have to be rolled for the velocity to be equal to 300 cm/s?
Name:
