Question

.. In 2000, the population of a country was approximately 5.73 million and by 2028 it is projected to grow to 8 million. Use the exponential growth model A=Age, in which t is the number of years after 2000 and A, is in millions, to find an exponential growth function that models the data, By which year will the population be 15 million? Population (millions) b. 12 Projected 9 2000 6 5,730,000 3- 0- 1950 1970 1990 2010 2030 2050 Year a. The exponential growth function that models the data is A= (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.)

Answer 1

Given in 2000 ) 5.73M O t nofyss afas 2000 substitute above value in ea o an 2028 &M kt A=Ao e In 2000 t=0 & A = 5.73M substituture above values in D, we're klo) 5.13= Ao e In 2028 t=28 ye } TA= 5.13 A = 8 m a8k 8 = Ao e 28k 8=5073 e 28k 8 1.39616=e (1.39646) Je 5.73 28 k = loge

28k = 0.33373 k= 0.33373 28. k=0001192 Hence O•OLLg2t A=5.13 € A = 15m then t=7 0.01192t 15 = 5.13 e od 1921 e = 2.6178 5.73 0.044 92 t = 2.61 18 de t = od 1192 (0896233) t = 80.7327 = 81yr =) In (2081) the population will be 15m