1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
bonufazy [111]
2 years ago
8

6. If the net investment function is given by

Mathematics
1 answer:
Pachacha [2.7K]2 years ago
6 0

The capital formation of the investment function over a given period is the

accumulated  capital for the period.

  • (a) The capital formation from the end of the second year to the end of the fifth year is approximately <u>298.87</u>.

  • (b) The number of years before the capital stock exceeds $100,000 is approximately <u>46.15 years</u>.

Reasons:

(a) The given investment function is presented as follows;

I(t) = 100 \cdot e^{0.1 \cdot t}

(a) The capital formation is given as follows;

\displaystyle Capital = \int\limits {100 \cdot e^{0.1 \cdot t}} \, dt =1000 \cdot  e^{0.1 \cdot t}} + C

From the end of the second year to the end of the fifth year, we have;

The end of the second year can be taken as the beginning of the third year.

Therefore,  for the three years; Year 3, year 4, and year 5, we have;

\displaystyle Capital = \int\limits^5_3 {100 \cdot e^{0.1 \cdot t}} \, dt \approx 298.87

The capital formation from the end of the second year to the end of the fifth year, C ≈ 298.87

(b) When the capital stock exceeds $100,000, we have;

\displaystyle  \mathbf{\left[1000 \cdot  e^{0.1 \cdot t}} + C \right]^t_0} = 100,000

Which gives;

\displaystyle 1000 \cdot  e^{0.1 \cdot t}} - 1000 = 100,000

\displaystyle \mathbf{1000 \cdot  e^{0.1 \cdot t}}} = 100,000 + 1000 = 101,000

\displaystyle e^{0.1 \cdot t}} = 101

\displaystyle t = \frac{ln(101)}{0.1} \approx 46.15

The number of years before the capital stock exceeds $100,000 ≈ <u>46.15 years</u>.

Learn more investment function here:

brainly.com/question/25300925

You might be interested in
Triangle ABC is translated 2 units down and 1 unit to the left. Then is rotated 90 degrees clockwise about the origin to form Tr
Colt1911 [192]
M∠A′B′C′ = m∠ABC would be the answer for this. if you could give me a pic, I could answer. I don't see Triangle ABC

8 0
3 years ago
Solve for x.<br> Help ASAP please!!!
sattari [20]

Answer:

The value of x is 4

Step-by-step explanation:

In a right triangle, if a segment is drawn from the right angle ⊥ to the hypotenuse like the given figure, then

∵ The length of one side of the right triangle = (x + 2)

∵ The length of the hypotenuse = x + 5

∴ (x + 2)² = x (x + 5)

∵ (x + 2)² = (x + 2)(x + 2)

∴ (x + 2)(x + 2) = x(x + 5)

→ Simplify the two sides

∵ (x)(x) + (x)(2) + (2)(x) + (2)(2) = (x)(x) + (x)(5)

∴ x² + 2x + 2x + 4 = x² + 5x

→ Add the like terms in the left side

∴ x² + 4x + 4 = x² + 5x

→ Subtract x² from both sides

∵ x² - x² + 4x + 4 = x² - x² + 5x

∴ 4x + 4 = 5x

→ Subtract 4x from both sides

∴ 4x - 4x + 4 = 5x - 4x

∴ 4 = x

∴ The value of x is 4

3 0
3 years ago
Horizontal, vertical, or neither?
Jobisdone [24]

The graph of the equation is a linear graph and is as represented in the attached image.

<h3>Graph of the equation:</h3>

According to the question;

  • The profit y (in dollars) for a business from selling x games is represented by; y = 33x.

In essence, the graph of the equation is a straight line graph with slope, m = 33.

The graph of the equation is therefore as represented in the attached image.

Read more on straight line graph;

brainly.com/question/14808962

4 0
2 years ago
Please help with this question?!?
erik [133]

Answer:

416 mi

Step-by-step explanation:

In order to find the surface area, you must find the area of each square. There are a total of 6 that make up the prism.

<em>Remember to find the area it is length x width</em>

  1. 9 x 8 = 72 which is the area for 4 of the squares. 2 on the side and 2 on the bottom
  2. Lastly for the last 2 squares to find the area you multiply 8 x 8 = 64
  3. In total, you will add 72+72+72+72+64+64 which equals 416

3 0
2 years ago
X + 2y – 4z = 1<br> -2x – 4y + 4z = 6<br> -4x – 3y – 4z = 21
elena55 [62]

Answer:

x = - 1

y = - 3

z = -2

Step-by-step explanation:

Please see steps in the image attached here.

6 0
3 years ago
Other questions:
  • What is 50% of 166%?
    14·2 answers
  • The angle addition postulate is sometimes described as "the whole is equal to the sum of its parts." Explain how this descriptio
    10·1 answer
  • What is 1.18 devided by 12
    14·2 answers
  • Mr. Taylor's 4th grade class uses Skittles to learn about probability. They open several randomly selected bags of Skittles and
    9·1 answer
  • f(x)=x^3-3x^2-9x+4 find the intervals on which f is increasing or decreasing b. find the local maximum and minimum values of f.
    7·1 answer
  • May i get help please?
    6·1 answer
  • 24 is equal to 25% of a number n. Write and solve an equation to find n. Write the percent as a decimal. Equation: $$ Solution:
    8·1 answer
  • Acil çözümünü yazın bana ​
    11·1 answer
  • There are 347 students going on a field trip. Each bus holds 44 students. If each bus costs $95, is the total cost of the buses
    14·1 answer
  • Question 7
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!