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17–20 MODELING, APPLICATIONS These problems will give you a first impression of modeling. Many more problems on modeling follow throughout this chapter. 17. Half-life. The half-life measures exponential decay. It is the time in which half of the given amount of radioactive substance will disappear. What is the half-life of 226/88Ra (in years) in Example 5? 18. Half-life. Radium 224/88Ra has a half-life of about 3.6 days. (a) Given 1 gram, how much will still be present after 1 day? (b) After 1 year? 19. Free fall. In dropping a stone or an iron ball, air resistance is practically negligible. Experiments show that the acceleration of the motion is constant (equal to g = 9.80 m/sec^2 = 32 ft/sec^2, called the acceleration of gravity). Model this as an ODE for y(t), the distance fallen as a function of time t. If the motion starts at time t = 0 from rest (i.e., with velocity v = y' = 0), show that you obtain the familiar law of free fall y = 1/2gt^2.

          17–20 MODELING, APPLICATIONS
These problems will give you a first impression of modeling. Many more problems on modeling follow throughout this chapter.
17. Half-life. The half-life measures exponential decay. It is the time in which half of the given amount of radioactive substance will disappear. What is the half-life of 226/88Ra (in years) in Example 5?
18. Half-life. Radium 224/88Ra has a half-life of about 3.6 days.
(a) Given 1 gram, how much will still be present after 1 day?
(b) After 1 year?
19. Free fall. In dropping a stone or an iron ball, air resistance is practically negligible. Experiments show that the acceleration of the motion is constant (equal to g = 9.80 m/sec^2 = 32 ft/sec^2, called the acceleration of gravity). Model this as an ODE for y(t), the distance fallen as a function of time t. If the motion starts at time t = 0 from rest (i.e., with velocity v = y' = 0), show that you obtain the familiar law of free fall
y = 1/2gt^2.

17–20 MODELING, APPLICATIONS
These problems will give you a first impression of modeling. Many more problems on modeling follow throughout this chapter.
17. Half-life. The half-life measures exponential decay. It is the time in which half of the given amount of radioactive substance will disappear. What is the half-life of 226/88Ra (in years) in Example 5?
18. Half-life. Radium 224/88Ra has a half-life of about 3.6 days.
(a) Given 1 gram, how much will still be present after 1 day?
(b) After 1 year?
19. Free fall. In dropping a stone or an iron ball, air resistance is practically negligible. Experiments show that the acceleration of the motion is constant (equal to g = 9.80 m/sec^2 = 32 ft/sec^2, called the acceleration of gravity). Model this as an ODE for y(t), the distance fallen as a function of time t. If the motion starts at time t = 0 from rest (i.e., with velocity v = y' = 0), show that you obtain the familiar law of free fall
y = 1/2gt^2.

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