Answer:
A) 63.36 years.
B) 100.42 years.
Step-by-step explanation:
We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.
A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.
![\frac{7.1 \times 2}{7.1} =(1.011)^{t}](https://tex.z-dn.net/?f=%5Cfrac%7B7.1%20%5Ctimes%202%7D%7B7.1%7D%20%3D%281.011%29%5E%7Bt%7D)
![2 =(1.011)^{t}](https://tex.z-dn.net/?f=2%20%3D%281.011%29%5E%7Bt%7D)
Now let us solve for t using logarithm.
![ln(2) =t \cdot ln(1.011)](https://tex.z-dn.net/?f=ln%282%29%20%3Dt%20%5Ccdot%20ln%281.011%29)
![t=\frac{0.6931471805599453}{0.0109399400383344}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B0.6931471805599453%7D%7B0.0109399400383344%7D)
![t=63.3593217267282743049\approx 63.36](https://tex.z-dn.net/?f=t%3D63.3593217267282743049%5Capprox%2063.36)
Therefore, it will take 63.36 years the population to be double.
B) Now we will find the number of years it will take the population to be triple of its size.
![7.1 \times 3=7.1(1.011)^{t}](https://tex.z-dn.net/?f=7.1%20%5Ctimes%203%3D7.1%281.011%29%5E%7Bt%7D)
![3 =(1.011)^{t}](https://tex.z-dn.net/?f=3%20%3D%281.011%29%5E%7Bt%7D)
Now let us solve for t using logarithm.
![ln(3) =t \cdot ln(1.011)](https://tex.z-dn.net/?f=ln%283%29%20%3Dt%20%5Ccdot%20ln%281.011%29)
![t=\frac{1.0986122886681097}{0.0109399400383344}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B1.0986122886681097%7D%7B0.0109399400383344%7D)
![t=100.4221490079915311298\approx 100.42](https://tex.z-dn.net/?f=t%3D100.4221490079915311298%5Capprox%20100.42)
Therefore, it will take 100.42 years the population to triple of its size.
Answer:
A. You may set the variables in either order. But for argument sake, let's set as follows:
x = Amount of bookshelves
y = Amount of tables
B. Because of the amount of things you need to make, the following is an inequality using those variables.
x + y > 25
Plus you can determine a second inequality based on the amount of money that you have to spend.
20x + 45y < 675
Finally you may also add in that each value must be greater than or equal to zero, since they cannot have negative tables.
C. By solving the system and looking at basic constraints when graphed, you can see the feasible region has 4 vertices.
(0,0)
(18, 7)
(0, 15)
(33.75, 0) or (33, 0) if you insist on rounding.
Step-by-step explanation: Good luck and hope this helps :)
Answer:
![3x^{4}](https://tex.z-dn.net/?f=3x%5E%7B4%7D)
Step-by-step explanation:
I suggest looking lessons on it online if you don't understand... It's hard to do your work especially if you don't understand it. Or if your online, go to past lessons or something.
Y+38°= 180 beacuse if a and b are parallel they are
co interior angles. This means that they will at to 180.
y=180-38= 142°
Answer: 142°
Drew out some hopefully helpful pictures below. Hope they help! let me know if you still have any questions!