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
<span>(a) y = 729.8x + 41431
(b) 80,000 shopping centers in about 2048.
(a) Since we only have 2 data points, let's create the equation of a line using slope intercept form where y = number of shopping centers and x = number of years since 1995. So the general form of the equation will be:
y = ax + b
Let's first calculate a, which is the difference in y divided by the difference in x, so
(48729 - 41431)/(2005-1995) = 7298/10 = 729.8
Now we have the equation
y = 729.8x + b
Substitute the values for a known pair and solve for b. I'll use the pair (0, 41431). The value 0 represents 0 years after 1995. So
y = 729.8x + b
41431 = 729.8*0 + b
41431 = 0 + b
41431 = b
So the desired equation is: y = 729.8x + 41431
(b) To answer this, substitute 80000 for y and then solve for x. So: y = 729.8x + 41431
80000 = 729.8x + 41431
38569 = 729.8x
52.84872568 = x
So the number of shopping centers will reach 80000 52.8 years after 1995, or about 2048.</span>
