In 2012, the population of a city was 6.57 million. the exponential growth rate was 2.87% per year. a) find the exponential growth function. b) estimate the population of the city in 2018. c) when will the population of the city be 10 million? d) find the doubling time. a) the exponential growth function is p(t)equals nothing, where t is in terms of the number of years since 2012 and p(t) is the population in millions

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.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c