Since the number of streetlights grows linearly in time, measured in months, we derive the expression for the number of streetlights below:
\(m = m_{o} + r\cdot n\) (1)
Where:
- \(m_{o}\) - Initial number of streetlights.
- \(r\) - Growth rate, in \(\frac{1}{mo}\)
- \(n\) - Time, in months.
If we know that \(m_{o} = 130\), \(m = 146\) and \(n = 4\), then the growth rate is:
\(r = \frac{m-m_{o}}{n}\)
\(r = \frac{146-130}{4}\)
\(r = 4\)
And if we know that \(m_{o} = 130\), \(m = 200\) and \(r = 4\), then the number of months is:
\(n = \frac{m-m_{o}}{r}\)
\(n = \frac{200-130}{4}\)
\(n = 17.5\)
a) The explicit formula for the number of lights is \(m = 130 + 4\cdot n\).
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
