Equivalent fractions to 1/3

6. If the net investment function is given by

Pachacha [2.7K]

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 298.87.

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

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 ≈ 46.15 years.

Learn more investment function here:

brainly.com/question/25300925

6 0

2 years ago

At the Manchester Golf Tournament, the leader board shows Farrah's score as 5 on the front nine and 8 on the back nine.

zvonat [6]

Farrah's total score for both rounds will be -3.

Since the leader board shows Farrah's score as 5 on the front nine, this will be: +5

Since the leader board shows Farrah's score as 8 on the back nine, this will be -8. Then we'll add both together to get the total score which will be:

= 5 + (-8)

= 5 - 8

= -3

His total score will be -3.

Read related link on:

brainly.com/question/24753023

7 0

2 years ago

5/10 points, 1 question ( no rude answers )

bagirrra123 [75]

The answer is b because all the points lie on the graph

3 0

3 years ago

Read 2 more answers

I need help with this

LiRa [457]

Answer:

Since

4

4x

and

4

n

have the same denominator, add them by adding their numerators.

Step-by-step explanation:

7 0

2 years ago

Solve for x: x + 8 = 15

love history [14]

Answer:

7

Step-by-step explanation:

x + 8 = 15

Subtracting 8 from both sides,

x = 15 - 8

=> x = 7

6 0

3 years ago