Answer:
a) ![\frac{dS}{dt}=S'(t)= 2(0.5) t +3 = t+3](https://tex.z-dn.net/?f=%20%5Cfrac%7BdS%7D%7Bdt%7D%3DS%27%28t%29%3D%202%280.5%29%20t%20%2B3%20%3D%20t%2B3)
b) ![S(4) = 0.5*(4^2) +3(4) -5=15 million](https://tex.z-dn.net/?f=%20S%284%29%20%3D%200.5%2A%284%5E2%29%20%2B3%284%29%20-5%3D15%20million)
c) For this case we have the total sales $ 15 millions after t =4 months
d) ![S'(4) = 4+3 = 7 million](https://tex.z-dn.net/?f=%20S%27%284%29%20%3D%204%2B3%20%3D%207%20million)
e) This value represent the increase in the amount of sales in millions after t=4 months
Explanation:
For this case we have the following function for the sales
![S(t) = 0.5 t^2 +3t -5](https://tex.z-dn.net/?f=%20S%28t%29%20%3D%200.5%20t%5E2%20%2B3t%20-5)
Part a
For this case we want to find the derivate of S respect to t and we got:
![\frac{dS}{dt}=S'(t)= 2(0.5) t +3 = t+3](https://tex.z-dn.net/?f=%20%5Cfrac%7BdS%7D%7Bdt%7D%3DS%27%28t%29%3D%202%280.5%29%20t%20%2B3%20%3D%20t%2B3)
Part b
For this case we want to find the value of S when t = 4 so if we replace we got:
![S(4) = 0.5*(4^2) +3(4) -5=15 million](https://tex.z-dn.net/?f=%20S%284%29%20%3D%200.5%2A%284%5E2%29%20%2B3%284%29%20-5%3D15%20million)
Part c
For this case we have the total sales $ 15 millions after t =4 months
Part d
For this case we just need to replace t=4 in the derivate and we got:
![S'(4) = 4+3 = 7 million](https://tex.z-dn.net/?f=%20S%27%284%29%20%3D%204%2B3%20%3D%207%20million)
Part e
This value represent the increase in the amount of sales in millions after t=4 months
Answer:
d. to regulate interstate commerce
Explanation:
The United States Constitution has the commerce clause in Article 1 Section 8 which allows the Congress to control the commerce with other nations and among the states.
According to this clause, the Congress can regulate the commerce that takes place between states and because of that, the answer is that the Constitution expressly grants the power to regulate interstate commerce to Congress.
Answer:
Ans. He must save during each of the following 10 years, at the end of each year $32,452.
Explanation:
Hi, in order to find the amount of money that he should have in ten years so he can receive an annual payment of $65,156 for 25 more years (24 payments), we need to bring to present value all 24 payments to year 10. Let me show you the formula.
![PresentValue_{10} =\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }](https://tex.z-dn.net/?f=PresentValue_%7B10%7D%20%3D%5Cfrac%7BA%28%281%2Br%29%5E%7Bn%7D-1%29%20%7D%7Br%281%2Br%29%5E%7Bn%7D%20%7D)
Where:
A= $65,156
n= 24
r= 0.08
Therefore the present value in year 10 is:
![PresentValue_{10} =\frac{65,156((1+0.08)^{24}-1) }{0.08(1+0.08)^{24} }=686,012](https://tex.z-dn.net/?f=PresentValue_%7B10%7D%20%3D%5Cfrac%7B65%2C156%28%281%2B0.08%29%5E%7B24%7D-1%29%20%7D%7B0.08%281%2B0.08%29%5E%7B24%7D%20%7D%3D686%2C012)
So that is our present value in year 10, or to put it in other words, our future value (if we look at it from year 0). Now we need to find the annuity (amount to save) that with account for $686,012, plus that $100,000 that he already has saved.
Every should look like this.
![686,012=100,000*(1+0.08)^{10} +\frac{A((1+0.08)^{10}-1) }{0.08(1+0.08)^{10} }](https://tex.z-dn.net/?f=686%2C012%3D100%2C000%2A%281%2B0.08%29%5E%7B10%7D%20%2B%5Cfrac%7BA%28%281%2B0.08%29%5E%7B10%7D-1%29%20%7D%7B0.08%281%2B0.08%29%5E%7B10%7D%20%7D)
And we solve this equation for "A".
![686,012=A(14.4865625)+215,892](https://tex.z-dn.net/?f=686%2C012%3DA%2814.4865625%29%2B215%2C892)
![A=\frac{(686,012-215,892)}{14.4865625} =32,452](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B%28686%2C012-215%2C892%29%7D%7B14.4865625%7D%20%3D32%2C452)
Best of luck.
A leadership is best described as the ability to influence a group toward the achievement of a vision or set of goals.
<h3>What is a
leadership?</h3>
In a formal setting, this refers to individual ability to influence, lead and guide others people to accomplish a predetermined mission in the manner desired.
Hence, it is best described as the ability to influence a group toward the achievement of a vision or set of goals.
Therefore, the Option D is correct.
Read more about leadership
<em>brainly.com/question/12522775</em>
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