Question

7 mark for review
the population of a town was 26,267 in the year 2000 and 26,668 in the year 2010. the equation (10x + 26,267 = 26,668) describes this situation. which of the following is the best interpretation of (x) in this context?
a the total increase in population between 2000 and 2010
b the projected population of the town 10 years after 2010
c the average increase per year of the population between 2000 and 2010
d the percentage by which the population of the town increased each year between 2000 and 2010

Explanation:

• Option A: The total increase in population between 2000 and 2010 is \(26668 - 26267 = 401\), which is not represented by \(x\) (since the equation has \(10x\)). So A is incorrect.
• Option B: The equation is about the population change from 2000 to 2010, not a projection 10 years after 2010. So B is incorrect.
• Option C: The time between 2000 and 2010 is 10 years. The equation \(10x + 26267 = 26668\) can be thought of as (average increase per year) \(\times\) (number of years) + initial population = final population. Solving for \(x\) gives the average increase per year over 10 years. So C is correct.
• Option D: The equation is linear (involving \(10x\), not a percentage - based growth formula like exponential growth which would involve percentages). So D is incorrect.

Answer:

C. The average increase per year of the population between 2000 and 2010