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?

Question

Mathematics

Nadia Marsh

23 October, 10:26

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?

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Answers (2)

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Blackjack · 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

Kendrick · Answer 2

13.5 months

146-130=16

16/4=4

200-146=54

54/4=13.5