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In 1977, the price of a scientific
calculator was $175. In 2004, the
price was $15. Assuming the change
in price was linear, what was the
approximate price of a scientific
calculator in 1998?

Sagot :

First, find the linear equation:

Let the x-axis represents the years and the y-axis represents the price.

1977 (y₁) = 0                                     Price in 1977 (x₁) = 175
2004 (y₂) = 2004 - 1977 = 27            Price in 2004 (x₂) = 15

The two points are:
(1997, price) = (0, 175)
(2004, price) = (27, 15)

y-y₁ = [tex] \frac{y _{2}-y _{1} }{x _{2}-x _{1} } [/tex] (x - x₁)

y - 175 = -160/27 (x - 0)

y = -160/27 (x) + 175

y = -5.93x + 175   (Linear Equation)
       
Note that the slope (-160/27 or -5.93) is negative because the price 
of the calculator is decreasing.      

To find the price of calculator in 1998:
x₃ = 1998 - 1977
x₃ = 21

Plug-in 21 to x₃:
y₃ = -5.92(x₃) + 175
y₃ = -5.92 (21) + 175
y₃ = -124.32 + 175
y₃ ≈ 50.68  or  $51

ANSWER:  The price of calculator in 1998 is $50.68 or $51.


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