SOLUTION: Direct deposit. The percentage of workers receiving direct deposit of their paychecks went from 32% in 1994 to 60% in 2004 (www.directdeposit.com). Let 1994 be year 0 and 2004 b

Question 172851This question is from textbook
: Direct deposit. The percentage of workers receiving direct
deposit of their paychecks went from 32% in 1994 to 60%
in 2004 (www.directdeposit.com). Let 1994 be year 0 and
2004 be year 10.
a) Write the equation of the line through (0, 32) and
(10, 60) to model the growth of direct deposit.
b) Use the accompanying graph to predict the year in
which 100% of all workers will receive direct deposit
of their paychecks.
c) Use the equation from part (a) to predict the year in
which 100% of all workers will receive direct deposit This question is from textbook

Answer by actuary(112) (Show Source): You can put this solution on YOUR website!
Use the point-slope form of a line to write the equation.
The slope m = (60-32)/(10-0) = 28/20 = 2.8
The point-slope formula is y-32 = 2.8*(x-0) = 2.8*x
y= 2.8*x + 32
Using the graph, the predicted year in which, 100% of the workers will receive their paychecks via direct deposit is 26.
Using the equation, y = 2.8*x + 32 to make the prediction, solve the equation
100 = 2.8*x + 32 for x
100-32 = 2.8*x
68 = 2.8*x
x = 68/2.8
x = 24.3 years from 1994 = 2018.3

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