In 19951995, there were 41 comma 43141,431 shopping centers in a certain country. in 20052005, there were 48 comma 72948,729. (a) write an equation expressing the number y of shopping centers in terms of the number x of years after 19951995. (b) when will the number of shopping centers reach 80 comma 00080,000?

The first thing you should do for this case is to use the following table to perform the equation of a line:
 y x
 41,431 1995
 48,729 2005
 We have then that the line that best fits this data is
 y = 729.8x - 1E + 06
 Then, to know in what year the number of shopping centers reaches 80,000 we must replace this number in the equation of the line and clear x:
 80000 = 729.8x - 1E + 06
 Clearing x
 x = (80000 + 1E + 06) / (729.8) = 1479.857495
 nearest whole number
 1480
 This means that after 1480 years, 80000 shopping centers are reached.
 Equivalently, this amount is reached in the year:
 1480 + 1995 = 3475
 In the year 3475
 answer
 (a) y = 729.8x - 1E + 06
 (b) In the year 3475