The population of a city is modeled by the exponential function ƒ (x) = 689,254 · 2.40.014x, where x is the number of years after 2000. In what year will the city's population exceed one million?

Step-by-step explanation:

Given the population of a city is modeled by the exponential function

ƒ (x) = 689,254 · 2.4e^0.014x, where x is the number of years after 2000

In order to determine the year that the city's population will exceed one million, we will substitute f(x) = 1,000,000 and find x first as shown:

1,000,000 = 689,254  2.4e^0.014x,

1000000/689,254  = 2.4e^0.014x,

1.4508 = 2.4e^0.014x,

1.4508 /2.4 = e^0.014x,

0.6045 = e^0.014x,

Apply ln to both sides

ln 0.6045 = lne^0.014x,

-0.5033 = 0.014x

x = -35.95

Since x cannot be negative, lets say x ≈ 36years

This means that the population will exceed one million after about 36 years. The year it will exceed this amount will be 2000+36 = 2036

Note that the exponential equation used was not correctly written but the same calculation can be employed for any exponential functions you might have.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: