Mathematics, 25.12.2019 03:31 jordonlewis

Demographic experts say that the population, p, of china, in billions, can be approximated by the function p = 1.15(1.014)^+where t is the number of years since the start of 1993. using this model, estimate how much faster the chinese population will be growing in 2016 than in 2003. (be sure to use enough decimal places (6 or more) in your calculations.) a) 3.64 million people / year b) 5.46 million people / year c) 5.1 million people / year

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Answer from: garzamatt7

a) 3.64 million people / year

Step-by-step explanation:

The population of China, in billions, is represented by the following function:

$P(t) = 1.15*(1.014)^{t}$

The growth rate of the population after the year t after 1993 is given by P'(t)

$P'(t) = 1.15*(1.014)^{t}*\ln{1.014}$

$P'(t) = 0.016*(1.014)^{t}$

2003

2003 is 10 years after 1993. So

$P'(10) = 0.016*(1.014)^{10} = 0.018387$

The growth rate is 2003 is 0.018387 billion people a year.

2016

2016 is 23 years after 1993. So:

$P'(23) = 0.016*(1.014)^{23} = 0.022029$

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 from: clairesmom

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.

$\dfrac{\text{d}{P}}{\text{d}t} = \dfrac{\text{d[1.15(1.014)}^{t}]}{\text{d}t} = 1.15(1.014)^{t}\ln (1.014) =P \ln(1.014)$

Let's make a table to keep the calculations straight

$\begin{array}{ccccc}\textbf{Year} & \mathbf{t} & \mathbf{(1.014)}^{\mathbf{t}} & \mathbf{P} & \mathbf{\textbf{d}P/{\text{d}}t}\\2003 & 10& 1.149 157 &1.321 531& 0.018 373\\2016 & 23& 1.376 806& 1.583 327&0.022 013 \\\end{array}\\$

(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.

Answer from: Quest

i'm not sure what you mean but in todays world there is a lot of women that are the bread winners in the family. there is a lot more single mothers now that are going back to get an education which is boosting the economy. i believe there has been a boost in the economy due to women the cosmetic industry is boosting, chemist, the sky is becoming the limit for women in todays economy. most women are also putting off having kids just to make sure they have a education. i don't know how these two relate though to scriptures because it's not the way the lord wanted it. the man is suppose to be the bread winner and due to social media and the easy access we have there is a lot of cheating going on.

step-by-step explanation:

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

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