Question

City A's population of 1115000 is decreasing at a rate of 15000 per year. City B's population of 698000 is increasing at a rate of 45000 per year. In how many years will the populations be equal? Form the equation and round the answer to the nearest whole number.

Answer 1

7 years

Explanation:

Let x be number of years the populations be equal

City A's population of 1115000 is decreasing at a rate of 15000 per year.

The population is decreasing at a constant rate so we use equation

y= mx + b

where m is the slope(rate), b is the initial population

m= -15000 (decreasing) , b= 1115000

y= -15000 x + 1115000

City B's population of 698000 is increasing at a rate of 45000 per year.

m= 45000 (increasing) , b= 698000

y= 45000 x + 698000

Now we set the equations equal and solve for x

45000 x + 698000 = -15000 x + 1115000

Add 15000 on both sides

60000 x + 698000 = 1115000

Subtract 689000 on both sides

60000 x = 417000

Divide by 60000 on both sides

x= 6.95

So after 7 years the population will be equal.