# 8.2 RATES

(2.2)

Consider the function, y = 40 - 35.e-0.2x at the interval (0,10)

1. Calculate:

a) The values of y for x = 0,1,2,3,4,5,6,7,8,9,10;

b) Represent graphically the function y at the interval (0,10) of x;

c) The variation, Δy, corresponding to the interval (1,2) of x;

d) The absolute mean rate of variation of y, amr(y), at the intervals (1,7), (2,5), (5,6) and (8,9) of x;

e) The absolute instantaneous rate of variation of y, air(y), at the points x = 3 and x = 4;

f) Calculate the relative mean rate of variation of y, r.m.r.(y), at the interval (8,9) in relation to the value of y corresponding to the initial point, to the final point and to the central point of that interval;

g) Calculate a relative instantaneous rate of variation of y, r.i.r.(y) at the central point of the interval (8,9).

2. Calculate the air(y) of the following functions:

a) y = 1 + 10x
b) y = x3 - 2x + 3
c) y = ex
d) y = ln x

3. Calculate the rir(y) of the following functions:

a) y = 4 + x
b) y = ex
c) y = 6 · e2x
d) y = a · x with a = constant

4. Calculate the air of the air(y) of y = 3x2 - 4x - 12

5. Given the function, y = 3 · e-1.8x verify that rir(y) = air(ln y)