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Analyzing Growth Trends: Liver Transplant Waiting Lists and Population Statistics

This article delves into critical data regarding the number of people awaiting liver transplants and population growth in India. It examines the current year’s statistics and projects future trends using mathematical formulas. We will analyze Newton’s Law of Cooling, outlining how temperature affects the cooling process of objects. Additionally, we'll discuss financial implications, such as savings and loan repayments, alongside a study of telecommuting trends in the USA, evaluating whether the function is logarithmic or exponential.

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Analyzing Growth Trends: Liver Transplant Waiting Lists and Population Statistics

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  1. Warm Up • Combine: • If

  2. is the year is # of people waiting Number of People Waiting for Liver Transplants: pg. 457 How many people are waiting for a liver transplant this year, according to the formula? What is the increase for next year? (3) When will the number of people reach 40,000?

  3. Continuous Growth • Population Growth of India: pg. 457 #79 • 1,220,200,000 (1.22 billion) in 2012

  4. Newton’s Law of Cooling (or warming!) • Final temperature of an object • Depends on the initial temperature of the object • The difference between the temperature of the area and the object • A base rate of cooling (which must be found using data) • And the time the object has been cooling (or warming)

  5. Complete the JoCo Coroner’s report: • 8:30 am Arrived on the scene • 9:00 am Victim body temperature is 85.7 F • Air temperature was constant 70F, Assume body temperature was 98.6o at time of death. • 9:30 am Victim body temperature is 82.8 F • TIME OF DEATH:

  6. How long to Save a Million Dollars? • How much will we put into savings each period? • What annual interest rate will we earn? • So what is our interest each month?

  7. What Monthly Payment for School Loan? • How much did we borrow? • What annual interest rate will we pay? • We are given 10 years to pay off the loan.

  8. What If We Double the Monthly Payment? • How long will it take to pay off the loan now?

  9. The Shape of Data

  10. What type of function is this?

  11. People Telecommuting in the USA by Year. • x is the year after 1990. • y is the number of people telecommuting in millions. • Graph the data, and decide whether this is a logarithmic or exponential function. • Write your regression function down: • According to this function, how many people will be telecommuting this year? • In what year will the number of people telecommuting reach 15 million, according to this data? Is this interpolation or extrapolation?

  12. Newton’s Coffee Room temp: 67o

  13. Newton’s Coffee pg. 451 Room temp: T0 = 67o My MISTAKE! I needed to read more carefully.

  14. Newton’s Coffee pg. 451 Room temp: T0 = 67o • D = 182 – 67 = 115o • Use: T(t) =T0 + Dat • Solve for a: (choose any data point) • 179 = 67 + 115a2 • a = 0.98687

  15. Newton’s Coffee pg. 451 • T(t) =67 + 115(0.987)t • When will the coffee reach 105o ?

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