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
Cathy uses 3/4 teaspoon of vanilla in a batch of cookies. How many teaspoons are needed for 8 batches of cookies
34kurt
6 teaspoons
3/4 * 8 is 24/4
24/4= 6
So you need 6 teaspoons
8 0
3 years ago
I have to simplify this. It says assume that all variables in the variable in the denominator are nonzero. Leave your answer in
ra1l [238]
I wish I could help u but I can’t
7 0
3 years ago
HELP!!!!!!!!!!!
erica [24]
Your answer would be (b.) because -2+-3=-5

3 0
3 years ago
Read 2 more answers
What is the value of x?
valkas [14]
These are vertical angles and they are equal

3x + 50 = 6x - 10
50 + 10 = 6x - 3x
60 = 3x
60/3 = x
20 = x <==

3 0
3 years ago
Read 2 more answers
Order the set of numbers from LEAST to GREATEST.
Alexeev081 [22]

A would be your answer.

(I am going to assume that the set of numbers are multiplied by exponents.)

To solve you just need to calculate each one. Note that for positive exponents you move the decimal point to the right and negative exponents you move the decimal point to the left.

2.7*10^{3}, 4.24*10^{-3} , 4.7*10^{2}, 4.3*10^{-2}

The first scientific notation would be equal to 2700 because you move the decimal point 3 places to the right, since the exponent is positive.

2.7*10^{3} =2700

The second scientific notation would be equal to 0.00424 because you move the decimal point 3 places to the left, since the exponent is negative.

4.24*10^{-3} =0.00424

The third scientific notation would equal 470 because you move the decimal point 2 places to the right, since the exponent is positive.

4.7*10^{2} =470

The last scientific notation would equal 0.043 because you move the decimal point 2 places to the left, since the exponent is negative.

4.3*10^{-2} =0.043

4 0
3 years ago
Other questions:
  • MO bisects angle LMN, angel LMO = 6x-20.angle NMO= 2x+32 find angle LMN?
    13·1 answer
  • How do you verify factoring is correct?
    6·1 answer
  • Please help, due today.. any guesses?!
    14·1 answer
  • Im drowning. pls help. ​
    14·1 answer
  • What is coefficient of the term 16x
    13·2 answers
  • YALL I NEED HELP ASAP!!
    9·1 answer
  • Henry will spend at most $30 on gifts. So far, he has spent $21. What are the possible additional amounts he will spend? Use c f
    13·1 answer
  • Help please Ima give BRAINLIST:)
    15·2 answers
  • Haley bought 2.5 pounds of almonds for $16.20. How much did she pay per pound for the almonds?
    13·1 answer
  • A patient has been prescribed 1 gram (g) of Drug A. The stock dose is available in 250 milligram (mg) tablets. How many tablets
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!