Question

according to a census, a towns population in 2010 was 4,127 people. - in 2011, the population increased by 6%. - in 2012, the population decreased by 2%. which expression represents the towns population at the end of 2012? a. $4,127 + 4,127 \cdot 0.04$ b. $(4,127 + 4,127 \cdot 0.06) + (4,127 + 4,127 \cdot 0.06) \cdot 0.02$ c. $(4,127 + 4,127 \cdot 0.06) - (4,127 + 4,127 \cdot 0.06) \cdot 0.02$ d. $4,127 - 4,127 \cdot 0.04$

Explanation:

Step1: Calculate 2011 population

The 2010 population is 4,127. A 6% increase means we multiply the original population by $1 + 0.06$ (since 1 represents the full original population, plus 6% as a decimal).
$$4127 \times (1 + 0.06) = 4127 + 4127 \times 0.06$$

Step2: Calculate 2012 population

The 2011 population decreases by 2%, so we multiply the 2011 population by $1 - 0.02$ (full population minus 2% as a decimal). Substitute the 2011 population from Step1:
$$(4127 + 4127 \times 0.06) - (4127 + 4127 \times 0.06) \times 0.02$$

Answer:

C. $(4,127 + 4,127 \cdot 0.06) - (4,127 + 4,127 \cdot 0.06) \cdot 0.02$