REVIEW OF KEY CONCEPTS

							                              REVIEW OF KEY CONCEPTS
                                Limits & Rates of Change
1. The amount of active ingredient of a medicine ingested by the body, A, in milligrams, is a
                                                             1 2
     function of time, t, in hours given by:   A  10(t        t ); t  [0,12] .
                                                             12

a) What does the slope of the function at any point P represent?
                                                       80
b) Estimate the slope of the tangent to A at P (4 ,       ) using a method of your choice.
                                                       3

2. Determine the instantaneous rate of change of y with respect to x at each given x-value.
                                                           1
a)   y  x 2  1, x  2                           d)   y     ,x  3
                                                         x 2
                                                         x 1
b)   y  x 2  4 x  4, x  1                     e) y       ,x 1
                                                         x 3
c)   y  1  x 3,x  0

3. If a ball is dropped from the top of a 150 metre cliff, then its height after t seconds
    and before it hits the ground, is h  150  4.9t .
                                                         2

a) Find the average velocity of the ball for the following time periods.
        i)     t  [2,3]
         ii)      t  [2,2.1]
         iii)     t  [2,2.01]
b) Determine the instantaneous velocity when t=2.

4. The population of a slow-growing bacterial culture can be represented by the function
     P (t )  t 2  0.7t  10 , where t is measured in seconds.     Find the rate of change of
     the population after 5 seconds.




ANSWERS:
1. a) rate at which the body is eliminating the medicine
    b) 10/3 mg/h

2. a) 4 b) 6      c) 0      d) -1    e) 1/8

3. a) -24.5 m/s; -20.09 m/s; -19.649 m/s
    b) -19.6 m/s

4. 9.3 bacteria/second




MCV 4U0 – Limits & Rates of Change