A town has a population which is growing linearly. In 1970 its population was 36,000 while in 1985 its population was 63,000. Find a formula for its population P(t), where t=0 corresponds to the year 1970.
do it in thousands
(0, 36) , (15,63)
(y-36)/x = (63-36)/15
You take it from there.
To find a formula for the population P(t), where t corresponds to the number of years after 1970, we can use the concept of linear growth.
We are given two data points: in 1970, the population was 36,000, and in 1985, the population was 63,000.
Let's define t = 0 as the year 1970. Since the population is growing linearly, we can assume that the population increases at a constant rate per year.
First, let's find the rate of growth. We can calculate the change in population from 1970 to 1985:
Change in population = Population in 1985 - Population in 1970
Change in population = 63,000 - 36,000
Change in population = 27,000
Next, we need to find the growth rate per year. We can divide the change in population by the number of years between 1970 and 1985:
Growth rate per year = Change in population / Number of years
Growth rate per year = 27,000 / 15 (since 1985 - 1970 = 15 years)
Growth rate per year = 1,800
Now that we have the growth rate per year, we can use it to determine the formula for the population P(t) at any given year t.
The formula for linear growth is: P(t) = P(0) + (growth rate per year) * t
Substituting the given values:
P(t) = 36,000 + 1,800t
So the formula for the population P(t) is P(t) = 36,000 + 1,800t, where t represents the number of years after 1970.