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
A new cookie cake company is offering a
gtnhenbr [62]

Answer:

200.96in^2

Step-by-step explanation:

If the 1st cookie cake is 8" for its diameter and the 2nd cookie cake will have twice the length diameter of the 1st cookie cake .You will do 2 × 8 to get the diameter of the 2nd cookie cake.

First cookie cake diameter is 8".

Second cookie cake's diameter is 16".

Since we need the radius to find the area of the 2nd cookie cake we're going to do 16 / 2 which equals 8 so 8 is the radius.

A=(pi)r^2

A=(pi)8^2 *to the 2nd power means times by the same number

A=(pi)64

A= (3.14)(64)

A=200.96

=200.96^2

pi= 3.14 *for this problem

7 0
3 years ago
Joan has 294 black marbles. Joan has 42 times more black marbles than Dan. How many black marbles does Joan has?
lara [203]
Joan has 294 marbles
dan has 7 marbles
5 0
3 years ago
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number o
Ksenya-84 [330]

Answer:

Step-by-step explanation:

Step1:

We have Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α =8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter μ = 8t

Step2:

Let “X” the number of small aircraft that arrive during time t and it follows poisson distribution parameter “”

The probability mass function of poisson distribution is given by

P(X) = , x = 0,1,2,3,...,n.

Where, μ(mean of the poisson distribution)

a).

Given that time period t = 1hr.

Then,μ = 8t

             = 8(1)

             = 8

Now,

The probability that exactly 6 small aircraft arrive during a 1-hour period is given by

P(exactly 6 small aircraft arrive during a 1-hour period) = P(X = 6)

Consider,

P(X = 6) =  

              =  

              =  

              = 0.1219.

Therefore,The probability that exactly 6 small aircraft arrive during a 1-hour period is 0.1219.

1).P(At least 6) = P(X 6)

Consider,

P(X 6) = 1 - P(X5)

                = 1 - {+++++}

                = 1 - (){+++++}

                = 1 - (0.000335){+++++}

                = 1 - (0.000335){1+8+32+85.34+170.67+273.07}

                = 1 - (0.000335){570.08}

                = 1 - 0.1909

                = 0.8090.

Therefore, the probability that at least 6 small aircraft arrive during a 1-hour period is 0.8090.

2).P(At least 10) = P(X 10)

Consider,

P(X 10) = 1 - P(X9)

                 = 1 - {+++++

5 0
3 years ago
mark's soup recipe makes 6 servings and uses 4 carrots and 2 potatoes. How many carrots and potatoes does he need for 15 serving
VLD [36.1K]
Let’s see, for 6 servings he needed 4 carrots, meaning every carrot was equal to 1.5 servings. 15/1.5 is 10, 10 carrots for 15 servings.
7 0
3 years ago
Let
kow [346]

Answer:

can write it again soon as you can do it again

6 0
2 years ago
Other questions:
  • On Friday afternoon, 560 people went to the local theater for the matinee. Youth tickets cost 5.75 and adult tickets cost 8.50.
    13·1 answer
  • Convert 13/10<br> to a mixed number.
    15·2 answers
  • The number y of cups of flour used to make x loaves of bread is represented by the equation y=3x. Graph the equation. what are t
    7·1 answer
  • A clipboard costs $2.23. It costs $0.58 more than a notebook. Sheila bought two clipboards and one notebook. She paid with a ten
    11·1 answer
  • I’ll give brainiest!
    13·1 answer
  • Write an inequality to describe the graph below ): tysm&lt;33​
    9·1 answer
  • Given a circle has a diameter of 12 inches, what is its area? *
    10·1 answer
  • U^3-512=()(u^2+8u+64)
    15·1 answer
  • Nancy is checking to determine if the expressions x + 4 + x and 6 + 2 x minus 2 are equivalent. When x = 3, she correctly finds
    15·2 answers
  • A trellis consists of overlapping wooden slats.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!