A worker is reviewing his pay increases over the past severa

A worker is reviewing his pay increases over the past several years. The table below shows the hourly wages W, in dollars that she earned as a function of time t, measured in years since the beginning of 2000.

a) Show that these data can be modeled by an exponential function by completing a table. Round your answers to two decimal places. Show your ratios.

b) The yearly growth factor for the data a=___?

c) What percentage raise did the worker receive each year?

d) The initial value of this function is _____? (include units)

e) Write a formula for this exponential function.

f) If this trend continues, what should the worker expect to earn per hour in 2008?

g) When should she expect to earn $30.50 per hour? Include a graph to support your answer. Be sure to label the axes as to what they represent and indicate your viewing window.

Solution

a)   y2/y1 = 16.47/15.25 = 17.79/16.47 =19.21/17.79 = 1.08 Ratio constant

So, data can be modelled by exponential function

b) Growth factor = 1+r = 1.08

c) Intial value = 15.25

d) Function W(t) = 15.25(1.08)^t

f) In 2008 ; t = 8

W(8) = 15.25(1.08)^8 = 28.189