Question #a73a3

1 Answer
Alex Boroda
May 21, 2015

Answer: #y = 0.25 * (1.0485)^t#

The exponential function will be #y=a*b^t#, where #a# is the initial value

So, #a=0.25# because the hourly minimum wage has the initial value of #$0.25# at the moment #t=0# (the year 1938).

(Verification: for #t=0#, #y=0.25*b^0# #=# #0.25*1 =0.25#)

In 2009, after 71 years, the value of the hourly minimum wage is $7.25. Therefore, #y=7.25# for #t=71#.

So, #7.25=0.25*b^71#

In order to find our exponential function, we have to find the value of #b#.

#b^71=7.25 / 0.25# #= 29# #=># #b=root71(29)# #~~1.0485#

Hence, our exponential function is #y=0.25*(1.0485)^t#

Based on this model, we can estimate the values of the hourly minimum wage for the other years, by substituting the values of #t# in the general formula:

  • for 2015, #t=77# #=># #y=0.25*(1.0485)^77~~9.5875#
  • for 2016, #t=78# #=># #y=0.25 * (1.0485)^78~~10.0525#

This is the graph of the function:
enter image source here

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