5. The value V in euro of a mobile phone after t years is given by V = k
( 1 __
2 ) , k is a constant. t
(a) Find k if the mobile phone is worth € 80 after 4 years. (b) Find its value after 5 years. (c) After how many years is it worth € 5?
(d) Plot a graph of V against t by copying and completing the following table:
t 012345 V
19.4 Intersecting exponential functions Y 11
ACTIVITY
ACTION Intersecting exponential functions
OBJECTIVE To plot two functions (where at least one is exponential) and to fi nd their points of intersection
Two functions f and g are defi ned as: f : x → 2 x , x ∈ R g : x → 2x + 1, x ∈ R
(a) Complete the table below and use it to draw graphs of f and g for 0 ≤ x ≤ 3 on the same diagram. x f
0 0·5 1 1·5 2 2·5 3 g
(b) Use the graphs to estimate the values of x for which 2 x – 2x – 1 = 0, correct to one decimal place.
(c) If 2 k = 5, use the graphs to estimate k and g (k), correct to one decimal place.
Solution f (x) = 2 x
g (x) = 2 x + 1 (a)
x f
0 0·5 1 1 1·4 2
1⋅5 2⋅8
2 4
2⋅5 5⋅7
3 8
g 1234567
To fi nd where two functions intersect, equate their y co-ordinates and solve for x or plot them on the same diagram and read off their points of intersection. EXAMPLE 5
