1159pm 7 of 10 9 complete 102517 900am 102717 500pm Assume t

11.59pm 7 of 10 (9 complete 10/25/17 9:00am 10/27/17 5:00pm Assume that the current population of a large region is 272 million. It was reported that the population grew 10.3% since the model A A et. Complete parts a through c below a. What was the population when it was measured 10 years ago? The population was million the first time it was measured. 10/30/17 11 59pm 10131/17 5:00pm-1: :11/09/17 11:59pm (Round to one decimal place as needed) b. What was the annual rate of growth between the two measurements? The annual rate of growth was 1% c. Assuming the same rate of growth. determine in how many years from the current year the region will have a populatio The region will have a population of 400 million years E(Round to-two decimal places as needed.) 11/09/17 11 59pm (Round up to the nearest year) 11:59pm

Solution

a) A = 272

k = 0.103

   t = 10 years

Now A = Ao*e^kt

272 = Ao*e^(0.103*10) ===========> Ao = 97.1 million

b) Population after one year = 97.1*e^(0.103*1) = 107.6 million

Annual growth rate = 10.8%

c) A = Ao*e^kt

400 = 97.1*e^(0.108*t) =======> t = 13.1 years