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, a. Find an explicit formula for the number of lights in month n b. How many months will it take to reach 200 lights?

Answer 1

Easy
find equation
y=mn+b
for n=0, y=130
130=m0+b
130=b

y=mn+130
also
n=4 for 146
146=4m+130
minus 130 both sides
16=4m
divide by 4 both sides
4=m


y=4n+130

find n for y=200

200=4n+130
minus 130 both sides
70=4n
divide both sides by 4
17.5=n

answer is 17.5 months

Answer 2

13.5 months

146-130=16

16/4=4

200-146=54

54/4=13.5