Answer:
a) 3.64 million people / year
Step-by-step explanation:
The population of China, in billions, is represented by the following function:
[tex]P(t) = 1.15*(1.014)^{t}[/tex]
The growth rate of the population after the year t after 1993 is given by [tex]P'(t)[/tex]
So
[tex]P'(t) = 1.15*(1.014)^{t}*\ln{1.014}[/tex]
[tex]P'(t) = 0.016*(1.014)^{t}[/tex]
2003
2003 is 10 years after 1993. So
[tex]P'(10) = 0.016*(1.014)^{10} = 0.018387[/tex]
The growth rate is 2003 is 0.018387 billion people a year.
2016
2016 is 23 years after 1993. So:
[tex]P'(23) = 0.016*(1.014)^{23} = 0.022029[/tex]
The growth rate is 2016 is 0.022029 billion people a year.
0.022029 - 0.018387 = 0.003642 = 3.642 million faster a year in 2016 than in 2003.
The correct answer is:
a) 3.64 million people / year
Answer:
a) 3.64 million people per year
Step-by-step explanation:
Let y = the year.
Then t = y - 1993
The rate of change of the function is the derivative with respect to t.
[tex]\dfrac{\text{d}{P}}{\text{d}t} = \dfrac{\text{d[1.15(1.014)}^{t}]}{\text{d}t} = 1.15(1.014)^{t}\ln (1.014) =P \ln(1.014)[/tex]
Let's make a table to keep the calculations straight
[tex]\begin{array}{ccccc}\textbf{Year} & \mathbf{t} & \mathbf{(1.014)}^{\mathbf{t}} & \mathbf{P} & \mathbf{\textbf{d}P/{\text{d}}t}\\2003 & 10& 1.149 157 &1.321 531& 0.018 373\\2016 & 23& 1.376 806& 1.583 327&0.022 013 \\\end{array}\\[/tex]
(0.022 012 855 - 0.018 373 122) billion = 0.003 64 billion = 3.64 million
So, the Chinese population in 2016 was growing by 3.64 million people per year faster than in 2003.
