The quadratic function f(x) = - 45x ^ 2 + 350x + 1.590mo models the population of a city, where x is the number of years after 2005 and f(x) the population of the city in thousands of people. What the estimated population of the city in 2015?

Population in year 2015 is 590 thousand people.

Step-by-step explanation:

Quadratic function that represents the population is

f(x) = -45x² + 350x + 1590

Here x = number of years after 2005

f(x) = Population of the city (in thousands)

We have to calculate the population of the city in year 2015.

So, duration or number of years from year 2005 = 2015 - 2005 = 10 years

Now we plug in the value x = 10 in the formula

f(10) = -45(10)² + 350(10) + 1590

       = -4500 + 3500 + 1590

       = 590 thousand people

Therefore, population in year 2015 is 590 thousand people.