Question

A town's population increases in one year from 100000 to 120000. If the population is growing linearly, at a steady rate, then what will the population be at the end of a second year?

Answer 1

If the population of a town increases linearly at a steady rate, we can use the formula for a linear relationship to determine the population at the end of a certain time period. Using the given information, the population at the end of a second year would be 140,000.

Step-by-step explanation:

If the population of a town increases linearly at a steady rate, we can use the formula for a “linear relationship” to determine the population at the end of a certain time period. The formula is: y = mx + b, where y is the dependent variable (population), x is the independent variable (time), m is the slope (rate of increase), and b is the y-intercept (initial population). In this case, the initial population is 100,000 and the population after one year is 120,000. Let's plug these values into the formula:

120,000 = m(1) + 100,000

Solving for m, we get:

m = 20,000

So, the slope or rate of increase is 20,000. Now we can use this rate to find the population after two years:

y = 20,000(2) + 100,000

y = 40,000 + 100,000

y = 140,000

Therefore, the population at the end of a second year would be 140,000.