Question

The number of streetlights in a town is growing linearly. four months ago (n = 0) there were 130 lights. now (n = 4) there are 146 lights. if this trend continues, how many lights will be installed at the end of the year (8 months from now)?

Answer 1

The number of lights at the end of the year can be determined using the linear growth rate. Using the formula y = mx + b, we can calculate the slope and find the number of lights for a given number of months.

Step-by-step explanation:

To find the number of streetlights that will be installed at the end of the year, we need to determine the growth rate. Given that the growth is linear, we can use the formula for a line: y = mx + b, where y is the number of lights and x is the number of months.

Using the points (0, 130) and (4, 146), we can calculate the slope, which represents the rate of increase in lights per month. The formula for slope is (y2 - y1) / (x2 - x1).

So, the slope is (146 - 130) / (4 - 0) = 16 / 4 = 4.

Now, we can find the number of lights at the end of the year (8 months from now) by plugging in x = 8 into the equation:

y = 4x + 130

y = 4(8) + 130

y = 32 + 130

y = 162

Therefore, there will be 162 lights installed at the end of the year.