It is important to be able to _______ a problem and _____

Point b represents an outcome in which select one:

Tatiana [17]

C.the economy is using all of its resources to produce books

8 0

3 years ago

When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t

liubo4ka [24]

Answer:

a) - r=5%: $S=$ 5,136.10$

- r=4%: $S=$ 4,885.61$

- r=3%: $S=$ 4,647.34$

b) - r=5%: t=14 years

- r=4%: t=17 years [/tex]

- r=3%: t=23 years [/tex]

c) The amount obtained is

- Compuonded quarterly: $5,191.83

- Compuonded continously: $5,200.71

The latter is always greater, since the more often it is capitalized, the greater the effect of compound interest and the greater the capital that ends up accumulating.

Explanation:

The rate of accumulation of money is

$dS/dt=rS$

To calculate the amount of money accumulted in a period, we have to rearrange and integrate:

$\int dS/S=\int rdt=r \int dt\\\\ln(S)=C*r*t\\\\S=C*e^{rt}$

When t=0, S=S₀ (the initial capital).

$S=S_0=Ce^{r*0}=Ce^0=C\\\\C=S_0$

Now we have the equation for the capital in function of time:

$S=S_0e^{rt}$

a) For an initial capital of $4000 and for a period of five years, the amount of capital accumulated for this interest rates is:

- r=5%: $S=4000e^{0.05*5}=4000*e^{0.25}= 5,136.10$

- r=4%: $S=4000e^{0.04*5}=4000*e^{0.20}= 4,885.61$

- r=3%: $S=4000e^{0.03*5}=4000*e^{0.15}= 4,647.34$

b) We can express this as

$S=S_0e^{rt}\\\\2S_0=S_0e^{rt}\\\\2=e^{rt}\\\\ln(2)=rt\\\\t=ln(2)/r$

- r=5%: $t=ln(2)/0.05=14$

- r=4%: $t=ln(2)/0.04=17$

- r=3%: $t=ln(2)/0.03= 23$

c) When the interest is compuonded quarterly, the anual period is divided by 4. In 5 years, there are 4*5=20 periods of capitalization. The annual rate r=0.0525 to calculate the interest is also divided by 4:

$S = 4000 (1+(1/4)(0.0525))^{5*4}=4000(1.013125)^{20}\\\\S=4000*1.297958= 5,191.83$

If compuonded continously, we have:

$S=S_0e^{rt}=4000*e^{0.0525*5}=4000*1.3= 5,200.71$

The amount obtained is

- Compuonded quarterly: $5,191.83

- Compuonded continously: $5,200.71

The latter is always greater, since the more often it is capitalized, the greater the effect of compound interest and the greater the capital that ends up accumulating.

5 0

3 years ago

Once the prototype of Wainwright Industries' new riding lawnmower, made especially for women, passes concept testing, the next s

Anastasy [175]

Answer: commercialization

Explanation:

Concept testing is the stage at which survey is being carried out for a particular product. This is done in order to know how consumers will accept a new product before such product is finally introduced to the market.

Since the product has passed the concept testing, the next step will be commercialization. This is when the product is then introduced and the business is managed in order to make profit.

8 0

2 years ago

Read 2 more answers

Crane Corporation was organized on January 1, 2020, with authorized capital of 502000 shares of $10 par value common stock. Duri

Finger [1]

Answer:

The amount of additional paid-in capital at December 31, 2020 is $97600.

Explanation:

Additional paid-in capital from stock issuance 31400*(13-10) 94200

Additional paid-in capital from treasury stock 3400*(14-13) 3400

Additional paid-in capital at December 31, 2020 97600

Therefore, The amount of additional paid-in capital at December 31, 2020 is $97600.

6 0

3 years ago

Which of the following does NOT describe the front-end business practices of firms that respect the strategic roles of purchasin

Blababa [14]

Answer:

b. Creativity does not require discipline.

Explanation:

Front end business practice is the strategy to develop and progress business activities from customer perspective. It focusses on customer demand and then products are customized according to customer needs. Marketing efforts are placed to inform customers about the different features of the product.

6 0

3 years ago

It is important to be able to _______ a problem and ______ it to the provider immediately

It is important to be able to _ a problem and it to the provider immediately