Question

The population in a certain town is increasing linearly each year. The population at time t=4 is 1580 and at time t=7 is 2000, where t is the number of years after 1990.

If P(t) is the population at time t, which of these equations correctly represents this situation?

Answer 1

We can use the two points given to find the slope of the line (which represents the population growth) and then use the point-slope form of the equation of a line to write an equation.

The population at time t=4 is 1580, which means P(4) = 1580. The population at time t=7 is 2000, which means P(7) = 2000. We can use these two points to find the slope:

slope = (P(7) - P(4)) / (7 - 4) = (2000 - 1580) / 3 = 140

So the slope of the line representing population growth is 140. Now we can use the point-slope form of the equation of a line to write an equation:

P - 1580 = 140(t - 4)

Simplifying and rearranging, we get:

P = 140t - 380

So the correct equation that represents the situation is:

P(t) = 140t - 380.