Linear equation word problems

Question

On January 1st, 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 1st, 2014 would 900 thousand buildings in the US have solar panels?

Answer 1

Or, putting it a little differently - each month the number increases by 180,000/12, or 15,000 buildings/mo.

The increase between the two building populations is 900,000 - 450,000 = 450,000. So it would take an addtional 450,000/15,000 = 30 months to increase from 450,000 to 900,000.

Answer 2

You have 450,000 buildings already. You are told that the rate of change (slope) is 180,000 buildings per 12 months

If t is the number of months after January 1st, 2014, then the total number N of buildings after t months is given by the linear equation

N(t) = (180000/12) * t + 450000

The question asks you to find the number of months it takes to get to 900000. This means we want to solve the following equation for t:

900000 = (180000/12) * t + 450000

450000 = (180000/12) * t

t = 12 * 450000 / 180000 = 30

Thus, it takes 30 more months.