In 2012 the population of a city was 6.55 million the exponential growth rate was 3.87% per year

A)

b)  

c)

d)

Step-by-step explanation:

a) The function of exponential growth for a population has the following formula:

In this equation:

is the initial population

r is the growth rate

t is the time in years

In this problem we know that

million in the year 2012.

So the equation is:

Where  represents the year 2012

b) If  in 2012, then in 2018

The population in 2018 is:

c) To know when the population is equal to 10 million we must equal P(t) to 10 and solve for t.

d) The function is doubled when

We solve for t.

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let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0