f(x) = __________ Suppose you have five children and they each have five children who each have five children and so forth. Write the function for this system. Use the variable x for the number of children.
__________ Use the above function for five children in every generation and WolframAlpha.com to determine the number of children in generation 4.
__________ The compound interest formula is given by:
For a principal P of $2000, an interest rate r of 0.04, compounded n = 5 times a year, calculate the amount A after a time t of ten years.
__________ The continously compounding interest formula is given by:
For a principal P of $2000, an interest rate r of 0.04, calculate the amount A after a time t of ten years.
__________ Super ball bounce heights are described by the function:
where x is the bounce number and f(x) is the bounce height. Evaluate this function at x = 10 bounces.
__________ Super ball bounce heights are described by the function:
where x is the bounce number and f(x) is the bounce height. Solve for the bounce number x where f(x) is two centimeters high .
Baby growth curve!
Age in months since conception
Actual pounds
9
6.7
13.3
13.5
17.5
15.5
21
20
26
17.6
27
19.4
37
23
57
29
The data in the table is actual data for my son from birth (age equals nine months) to four years old (57 months: 4 × 12 + 9). Plot this data using a LibreOffice.org Calc spreadsheet. Add in a logarithmic trend line. Write the logarithmic trend line below (round to two decimal places):
__________ Use the logarithmic function to determine the estimated weight of my son at x = 45 months.
__________ Use the logarithmic function to calculate the age of my son when his weight was equal to 10 pounds.
_______________ Solve 5(8x) = 2560 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.
Based on presentations in class, which of the three mathematical equations best models the distance verus speed for a sprinter?
_______ Using the best mathematical model for a sprinter that you chose above, calculate the speed of the sprinter at a distance of eleven meters.
_______ Using the best mathematical model for a sprinter, calculate the distance at which the sprinter has a speed of 4 m/s (Dana's top speed on a RipStik!).
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?
__________ Consider the exercise on the lawn on Monday. If the radius had been 1200 cm and the arc length was 3770, calculate the angle in radians for the semi-circular arc based on this data.
_________ Calculate: 300 sin(45°)
_________ Calculate: 300 cos(45°)
Suppose I want to inscribe a square inside a circle with a radius of 300. What will be the SVG coordinates of the four corners?
Name: