In 2000, the population of a country was approximately 6.31 million and by 2069 it is projected to grow to 12 million. Use the exponential growth model Upper A equals Upper A 0 e Superscript kt, in which t is the number of years after 2000 and Upper A 0 is in millions, to find an exponential growth function that models the data. b. By which year will the population be 7 million?

Step-by-step explanation:

This is your exponential growth function for population:

  and these are your initial conditions with the year 2000 being t = 0

(0, 6.31) and (69, 12)

We will use those values to find the equation that models this population growth.  In the coordinates, the first number is the time in years, t; the second number is the population after a certain time t goes by.  In other words, the second number represents the A in our model.  Using those values from the first set of coordinates will help us solve for A₀:

 which is basically e raised to the power of 0 which is equal to 1, so we get from that first set of coordinates that A₀ = 6.31

Now we will use that along with the numbers in the second coordinate pair to find the value for k:

Begin by dividing both sides by 6.31 to get

 and take the natural log of both sides since natural logs and e's undo each other:

 Simplifying both sides give us:

.6427709734 = 69k so

k = .0093155

Now we can finally write the equation that models this population as

and we can answer the question about which year, x, will the population be 7 million, A.

Begin by dividing both sides by 6.31 to get

and again take the natural log of both sides:

and simplify to

.1037744728=.0093155t so

t ≈ 11

That means that in the year 2011 the population will be 7 million

think about the doctor who treated the major and the speaker in the short story "in another country." put yourself in the shoes of the doctor, and based on what you read in the story, write what you think his thoughts about the major and the speaker would be. use the following vocabulary in your response and change the form of these words as needed: detached resign withered