Question

The population, P, of survey since 1995 can be estimated by the equation $P = 1.0635x + 3,250$ where x is the number of years since 1995 and $0 \leqslant x \leqslant 20$. In the context of this equation, what does the number $1.0635$ mostly like represent?
A) The estimated population of town Y in 1995
B) The estimated population of town Y in 2015
C) The factor by which the population of town Y increased yearly
D) The factor by which the population of town y decreased yearly

Answer 1

Here it is a given that, the city population represented by P, a survey of the population is expressed in question in a linear transformation. We have to find the required term that represents which context. By analyzing the given particular options to question we will get the required solution. We are going to solve this problem by eliminating the given particular options to find the solution.

Complete step-by-step solution:
According to our given in the question, P represents the population of the city.
The given relation is $P = 1.0635x + 3,250$ where $0 \leqslant x \leqslant 20$.
The number of years since 1995.
We have to find the term’s $1.0635$ representation
The outcome of the entire equation has something to do with the population.
Hence, the estimated population doesn’t represent the required number.
Because $1.0635$ can’t represent the population if P does.
$\therefore$ We will eliminate the options (A) and (B).
Let us consider the given expression,
That is, the expression with the operations are multiplication and addition, which means that over time the population would increase. There are no chances of a decrease in the city population.
So, we will eliminate the option (D).
And also by using same sense that,
The expression with the operations are multiplication and addition, which means that over time the population would increase.
Which means over time the population would increase.
Hence, the number $1.0635$ mostly like represents the factor by which the population of town Y increased yearly

$\therefore$ The option (C) is the correct answer.

Note: Population growth is determined by fertility rates-fatality rates. Birth rates and mortality rates are, in turn, determined by a combination of factors. Often economic growth and economic development have led to a decline in population growth, but there are no hard and fast rules and other factors, such as availability of family planning, social expectations and government intervention can play an important role.