Chapter 1.8, Problem 41P

The population of a particular village can be modeled by the equation $y=110x+56$

where $x$ is the number of years since 1990. In what year were there 1706 people living in the village?

To determine

To determine the year in which number of people were 1706.

Answer to Problem 41P

In 2005 the population was 1706.

Explanation of Solution

Given information :

The population of village is modeled by the equation $y=110x+56$

Where x is number of years since 1990.

Here we have to find year when total population was 1706.

Hence we put $y=1706$ in the given equation to determine the number of years.

Hence we get,

  $\begin{array}{l}1706=110x+56\\ 110x=1706-56\\ 110x=1650\\ x=\frac{1650}{110}=15\end{array}$

Therefore the population will become 1706 after 15 years from 1990.

Hence the year is 1990+15=2005