In 2012 the population of a city was 5.92 million in exponential growth was 2.77% per year find the exponential growth function

The exponential growth function is

Step-by-step explanation:

Given:

Initial population of a city is,

Exponential growth rate is,

Let the population for a given year 'x' be millions.

Now, the exponential growth of a population is given as:

Plug in 5.92 for and 0.0277 for . This gives,

Therefore, the exponential growth function is .

Using this equation, f(3) = 23.

In order to find the value of f(3), we need to take the f(x) equation and put 3 everywhere we see x. Then we follow the order of operations to solve. So, let's start with the original. 

f(x) = 2x^2 + 5sqrt(x - 2) 

Now place 3 in for each x. 

f(3) = 2(3)^2 + 5sqrt(3 - 2)

Now square the 3.

f(3) = 2(9) + 5 sqrt(3 - 2)

Do the subtraction inside of the parenthesis. 

f(3) = 2(9) + 5sqrt(1)

Take the square root

f(3) = 2(9) + 5(1)

Multiply. 

f(3) = 18 + 5

And add. 

f(3) = 23