Question

The population in a certain town is increasing linearly each year. the population at time t=3 is 1285 and at time t=8 is 2460, where t is the number of years after 1990.

if p(t) is the population at time t, write the equation below that correctly represents this situation.
Select the correct answer below:
O P(t) = 235t + 580
O P (t) = 240t + 540
O P(t) = 240t + 565
O P(t) = 230t +595
O P(t) = 230t + 620
O P(t) = 235t + 610

Answer 1

The correct linear equation for the population growth is P(t) = 235t + 580, found by calculating the slope between the two given points and forming an equation in point-slope form.

Step-by-step explanation:

To find the correct linear equation for the population growth, we need two points in the form (t, P(t)), which are given as (3, 1285) and (8, 2460). We will use the slope formula to find the rate at which the population increases.

The slope (m) is given by the change in population over the change in time, so:

m = (2460 - 1285) / (8 - 3) = 1175 / 5 = 235

Now, we'll use one of the given points and the slope to write the equation in point-slope form, which is:

P(t) - P1 = m(t - t1)

Substituting the point (3, 1285) and the slope 235, we get:

P(t) - 1285 = 235(t - 3)

Expanding the right side, we get:

P(t) - 1285 = 235t - 705

Adding 1285 to both sides to solve for P(t), we find:

P(t) = 235t + (1285 - 705)

P(t) = 235t + 580

Therefore, the correct equation that represents the situation is P(t) = 235t + 580.