4. The light produced by high-pressure sodium vapor streetlamps for different en

ID: 2896572 • Letter: 4

Question

4. The light produced by high-pressure sodium vapor streetlamps for different energy usages is shown in the table.

High-Pressure Sodium Vapor Streetlamps:

Energy Use (watts) 35 50 70 100 150

Light Output (lumens) 2250 4000 5800 9500 16,000

a. Find a quadratic model for the light output with respect to energy use.

b. Find a linear model for the light output with respect to energy use.

c. Apply each model to estimate the light output in lumens of a 200-watt bulb.

d. Which model gives the better estimate? Explain.

The quadratic model for light output :y= ax^2 +bx +c

2250 = a(35)^2 + 35b +c ------(1)

4000 = a(50)^2 +50b + c -------(2)

5800 = a(70)^2 +70b +c --------(3)

a) On solving the above we get: a = -16/21 ; b = 1270/21 ; c= -9500/3

-16x^2/21 +1270x/21 -9500/3

b) Linear model :( 35, 2250) and ( 50 , 4000)

slope = (4000-2250)/(50-35) = 1750/-15 =- 116.67

y = mx +c ----(use point 35, 2250 )

2250 = 35(-116.67) +c---> c= 6333.33

y = -1750x/15 + 6333.33 ---->( linear model)

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