Question

Officials project that between 2010 and 2050, the population of a certain city will drastically change. The model below gives the projection of the city's population , P, in thousands, with respect to time, t, in years, where 2010 corresponds to t = 0.P=175 + (11/2)tWhat does the 175 mean in the equationin 2010 the population of the city was 175 thousand
in 2050 the population of the city will be 175 thousand
Between 2010 and 2050, the population of the city will increase by 175 thousand
Between 2010 and 2050 the population of the city will decrease by 175 thousand

Answer 1

Answer:

In the year 2010, the population of the city was 175,000

Step-by-step explanation:

If we rewrote this as a linear expression in standard form (it is linear, btw), it would look like this:

$P(t)=\frac{11}{2}t+175$

The rate of change, the slope of this line, is 11/2.  If the year 2010 is our time zero (in other words, we start the clock at that year), then 0 time has gone by in the year 2010.  In the year 2011, t = 1 (one year goes by from 2010 to 2011); in the year 2012, t = 2 (two years have gone by from 2010 to 2012), etc.  If we plug in a 0 for t we get that y = 175,000.  That is our y-intercept, which also serves to give us the starting amount of something time-related when NO time has gone by.