In 1993, there were 41,778 shopping centers in a certain country. In 2003 , there were 48,103 . (a) Write an equation expressing the number \( y \) of shopping centers in terms of the number \( x \) of years after 1993 . (b) When will the number of shopping centers reach 70,000 ? (a) The equation is \( y=\square x+\square \). (Type integers or decimals.) (b) The number of shopping centers will reach 70,000 in the year \( \square \). (Round down to the nearest year.)

To determine the equation for the number of shopping centers and project the future growth, follow this engaging breakdown: (a) From 1993 to 2003, the number of shopping centers increased from 41,778 to 48,103. This shows a growth of 6,325 centers over 10 years. Therefore, the annual increase is \( 6,325 / 10 = 632.5 \). Given that \( x \) represents the number of years after 1993, the equation becomes \( y = 632.5x + 41,778 \). (b) To find when the shopping centers will reach 70,000, set the equation to 70,000: \[ 70,000 = 632.5x + 41,778 \] Now, solving for \( x \): \[ 632.5x = 70,000 - 41,778 = 28,222 \] \[ x = 28,222 / 632.5 \approx 44.6 \] Rounding down, \( x = 44 \). Thus, adding 44 years to 1993, the number of shopping centers will reach 70,000 in the year \( 1993 + 44 = 2037 \).