a. In​ 2000, the population of a country was approximately 6.45 million and by 2

Question

	In​ 2000, the population of a country was approximately	6.45	million and by	2060	it is projected to grow to	11	million. Use the exponential growth model	A=A0ekt​,	in which t is the number of years after 2000 and	A0	is in​ millions, to find an exponential growth function that models the data.
b.	By which year will the population be	15	​million?
195019701990201020302050036912YearPopulation (millions)2000:	6,450,000	Projected

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A coordinate system has a horizontal axis labeled Year from 1950 to 2050 in increments of 20 and a vertical axis labeled Population in millions from 0 to 12 in increments of 3. From left to right, a line rises at a constant rate from (1950, 1.5) to (1990, 5). The line then rises at a faster rate to the point (2010, 8). Lastly, the line rises at a rate similar to the first rate to the point (2050, 10). All coordinates are approximate. The label 2000: 6,450,000 is shown on the line near the year 2000. The label Projected is shown on the final portion of the line.

Question content area bottom

Part 1

a. The exponential growth function that models the data is

A=enter your response here.

​(Simplify your answer. Use integers or decimals for any numbers in the expression. Round to two decimal places as​ needed.)

Part 2

b. The​ country's population will be

15

million in the year

enter your response here.

​(Round to the nearest year as​ needed.)

Answer 1

6.45 million in 2000

11 million 60 years later in 2060

A=Pe^rt

11= 6.45e^60r

solve for r

60r = ln(11/6.45)

r = ln(11/6.45)/60

r =about 0.89% annual growth rate

pop= 6.45e^.89t where t = years after 2000

15=6.45e^.0089t

t= ln(15/6.45)/.0089=about 94.8

= the year 2095