Question

The quadratic function f (x) = - 45x2 + 350x + 1,590 models the population of a city where x represents the number of years since 2005 and f (x) is the population of the city in thousands of people. What is the estimated population of the city in 2010?

Answer 1

Answer: 2,215,000

Explanation:

Given: The quadratic function
`f (x) = - 45x^2 + 350x + 1,590` models the population of a city where x represents the number of years since 2005.

To Find: population of the city in 2010

We need to put x= 2010-2005 = 5

`f (5) = - 45(5)^2 + 350(5) + 1,590\\\\=-1125+1750+1590 =2215`

Hence, the estimated population of the city in 201 = 2215 thousands or 2,215,000 .