Exercises

Solve these two real-world problems

  1. The radioactive decay of uranium-235 can be described by the expression .
    Assign the expression to a variable.
    Use the subs command and plug = 9.9e-11 [yrs-1] into the expression.
    Use the subs command again to evaluate the expression at t=4.5e9 [yrs] (the age of the earth).
    Your solution will indicate the percentage of U-235 remaining from the creation of the Earth.
    Continue to use the subs command and plug in values of t to find the time when there will only be approximately 10% of the original U-235.

    Enter expr, subs, evalf

    Several subs and evalf to find t=2.32e10 for Uranium at 10 percent

  2. Suppose you throw a baseball straight up into the air. You could model the height of the baseball as function of time using the equation . Where h is the distance from the ground to the baseball, t is the time the ball has traveled, g is the acceleration due to gravity, v is the initial velocity, and y is the initial height of the baseball.

    Using the subs command to find h at t=9/2 seconds if g=98/100 m/s^2, v=20 m/s and y=3/2 m. Then use the evalf command to express your solution numerically.

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