Help me answer this question!!

Question

The population of Canada in 2010 was 35 million, and it grew 12.33% since 2000.

a. What was the population of Canada in 2000?

b. What was the annual rate of growth between 2000 and 2010?

c. Assuming the same rate of growth, determine the time from 2010 until Canada’s population doubles.

d. Find the time from 2010 until Canada’s population reaches 50 million.

Answer 1

A = Pe^rt where P = initial population, A = popluation after t years from 2000. r = growth rate

35 =Pe^.1233(10) = Pe^12.33

35/P = e^12.33

ln(35/P) = 12.33

ln35-lnP = 12.33

lnP = ln35-12.33 = about -8.7747

P = about e^--8.7747 = about1/6468.5= .00015459 million = .15459 thousand = 155

A= 155e^12.33 = 35 million

In 2000 there were just 155 people if it grew at the rate of 12.33% annually. which seems a little unrealistic.

The question seems to say 12.33% in 10 years, not an annual growth rate. That means

1.1233P = 35

P = 35/1.1233 = 31.1582 million in 2000

35 = (35/1.1233)e^10r

1.1233 = e^10r

ln1.1233 = 10r

r = ln1.1233/10 = .01163= 1.163% annual population growth

2 = e.01163t where t is the doubling time

ln2 = 0.1163t

t = (ln2)/.1163 = about 5.96 years

50 = 35e^rt = 35e^.1233t

ln(50/35) = .1233t

t = ln(10/7)/.1233 = about 2.89 years

t = about 3 years after 2010

in about 2013, population reached 50 million

2010, 35 million

2011, 35(1.1233) = 39.3

2012, 39.3(1.1233) = 44.2

2013 44.2(1.1233) = about 50 million