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?

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 Link

xero099 xero099 · Answer 2 · 2021-10-26T14:01:04+02:00

Since the number of streetlights grows linearly in time, measured in months, we derive the expression for the number of streetlights below:

[tex]m = m_{o} + r\cdot n[/tex] (1)

Where:

[tex]m_{o}[/tex] - Initial number of streetlights.
[tex]r[/tex] - Growth rate, in [tex]\frac{1}{mo}[/tex]
[tex]n[/tex] - Time, in months.

If we know that [tex]m_{o} = 130[/tex], [tex]m = 146[/tex] and [tex]n = 4[/tex], then the growth rate is:

[tex]r = \frac{m-m_{o}}{n}[/tex]

[tex]r = \frac{146-130}{4}[/tex]

[tex]r = 4[/tex]

And if we know that [tex]m_{o} = 130[/tex], [tex]m = 200[/tex] and [tex]r = 4[/tex], then the number of months is:

[tex]n = \frac{m-m_{o}}{r}[/tex]

[tex]n = \frac{200-130}{4}[/tex]

[tex]n = 17.5[/tex]

a) The explicit formula for the number of lights is [tex]m = 130 + 4\cdot n[/tex].

b) It will take 18 months to reach 200 streetlights.

We kindly invite to check this question on linear functions: https://brainly.com/question/3400735