Paper Homework Name: 1.2 Linear Functions 5. It has been found that for every ho

Question

Paper Homework Name: 1.2 Linear Functions 5. It has been found that for every hour spent weightless a person's reaction time increases. After 1 hour average reaction time is 0.35 seconds and after 6 hours it is 1 second. a) Find a model giving a person's reaction time Ras a function of t, the number of hours spent weightless. b) What would their reaction time be if they had been weightless 2 hours? c) How much would reaction time increase if they stayed weightless an additional 4 hours? d) If a person had a reaction time of 4 seconds estimate how many hours the person spent weightless. e) Find and interpret the vertical intercept of your model.

Explanation / Answer

we have two points ( 1 , .35 ) and ( 6 ,1 )

a) finding model for the situation

slope = ( 1 - .35 ) / ( 6 -1 )

slope = .13

hence , model is

R = 0.13t + 0.22

b) reaction time for 2 hours

R = 0.13 (2) + 0.22 = 0.48 seconds

c) R = 0.13 ( 4) + 0.22 = 0.74

so reaction time increases by .26 seconds

d) 4 = 0.13 t + 0.22

t = 29.08 hours

e) vertical intercept = 0.22 which means initial reaction time was 0.22 seconds

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