write the equation for this situation the population, p, in thousands,can be approximated by the sum of 4 and one-half times the years since 1985,d. Then graph the equation and use the graph to determine the population in the town in 1995.
To write the equation for this situation, we are given that the population, p, in thousands, can be approximated by the sum of 4 and one-half times the years since 1985, d.
Based on this information, we can write the equation as follows:
p = 4 + 0.5d
This equation states that the population, p, is equal to 4 plus 0.5 times the number of years since 1985, d.
To graph this equation, we need to determine the range of values for d that we want to consider. Let's assume we are interested in the years between 1985 and 2020. With this in mind, we can choose a range of values for d, such as 1985 to 2020.
Now, let's create a table of values by plugging in values of d and calculating the corresponding values of p:
| d | p |
| ---- | ---------- |
| 1985 | 4 |
| 1990 | 4 + 0.5(5) |
| 1995 | 4 + 0.5(10)|
| 2000 | 4 + 0.5(15)|
| 2005 | 4 + 0.5(20)|
| 2010 | 4 + 0.5(25)|
| 2015 | 4 + 0.5(30)|
| 2020 | 4 + 0.5(35)|
Now, let's plot these points on a graph with years (d) on the x-axis and population (p) on the y-axis. Connect the points with a line to get a graph of the equation.
By inspecting the graph, we can determine the population in the town in 1995. Locate the point on the graph where d = 1995 and read the corresponding value of p. This will give us the approximate population in thousands in the town in 1995.