The amount of taxes a city collect is proportional to the population of the city. If the city...

Question:

The amount of taxes a city collect is proportional to the population of the city.

If the city collects $6 billion in 1982 when the population was 2 million people, how much did the city collect in 1990 when the population was 3 million people? Proportionality When the amount of one quantity is proportional to another quantity, we can write a statement relating them. This statement involves some constant of proportionality, k. {eq}y = kx {/eq} Answer and Explanation: Since the amount of tax collected is proportional to the population, we can construct a statement relating these quantities through a constant of proportionality, k. {eq}T = kp {/eq} Since we know that$6 billion in taxes were collected when the population was 2 million people, we can find this constant of proportionality as follows.

{eq}6000000000 = k(2000000)\\ k = \frac{6000000000}{2000000} = 3000 {/eq}

Thus, we can use this to find the amount of tax collected when the population is 3 million people.

{eq}T = 3000(3000000) = 9000000000 {/eq}

Therefore, \$9 billion in taxes were collected in 1990 when the population was 3 million people.