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.

First

A)fails the vertical line test at (2,3) and (2,-2)

Second

B) not a function

Further Explanation:

It is possible to pass a single vertical line through this red curve. So it is not a function because it fails the vertical line test. One specific line goes from (2,3) to (2,-2) but there are infinitely other lines to choose from. In order to pass the vertical line test, it must be impossible to pass a vertical line through more than one point on the curve. A function is where any given input leads to exactly one output. In the case of (2,3) and (2,-2), the input x = 2 leads to more than one output (y = 3 and y = -2) at the same time