The price P in euro of a stock t months after its launch on the stock market is described by the linear function on the graph shown. The launch price is € 1·50.
Find a formula relating P to t and use it to fi nd P when t = 3⋅5 months.
P €
1 2 3
0 (6, 3) (0, 1·5) 1 2 Months 3 4 5
Solution Two points on the line: (0, 1·5), (6, 3)
Slope m = 3 − 1⋅5 ______
6 − 0 = 1⋅5 ___
EXAMPLE 9
As a diver descends in the ocean, the pressure P in Pascals (Pa) increases linearly with depth h in metres (m) from its pressure at the surface. If the pressure at the surface is 1 × 105 Pa and is 1·98 × 105 Pa at a depth of 10 m, fi nd the equation of the straight line connecting P and h.
(a) Find the pressure at a depth of 20 m.
(b) The safe depth to which a diver can descend is the depth at which the pressure is 3·75 × 10 5 Pa. What is this depth, correct to two decimal places?
