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On January $18$ , $2014$ , approximately $450$ thousand buildings in the United States (US) had solar panels. This number increased by a total of about $180$ thousand over the next $12$ months. Assuming a constant rate of change, approximately how many months after January $15$ , $2014$ would $900$ thousand buildings in the US have solar panels?

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Exponential growth and decay: word problems

Full solution

Q. On January

18

,

2014

, approximately

450

thousand buildings in the United States (US) had solar panels. This number increased by a total of about

180

thousand over the next

12

months. Assuming a constant rate of change, approximately how many months after January

15

,

2014

would

900

thousand buildings in the US have solar panels?

Determine Initial Number: Step $1$ : Determine the initial number of buildings and the increase over $12$ months. $\newline$ Initial buildings = $450,000$ $\newline$ Increase over $12$ months = $180,000$
Calculate Monthly Rate: Step $2$ : Calculate the monthly rate of increase. $\newline$ Monthly increase = $\frac{180,000 \text{ buildings}}{12 \text{ months}} = 15,000 \text{ buildings/month}$
Calculate Total Increase: Step $3$ : Calculate the total increase needed to reach $900,000$ buildings. $\newline$ Target = $900,000$ buildings $\newline$ Current = $450,000$ buildings $\newline$ Increase needed = $900,000 - 450,000 = 450,000$ buildings
Calculate Number of Months: Step $4$ : Calculate the number of months needed to reach the target. $\newline$ Months needed $= \frac{\text{Increase needed}}{\text{Monthly increase}} = \frac{450,000 \text{ buildings}}{15,000 \text{ buildings/month}} = 30 \text{ months}$

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