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Kipish [7]
2 years ago
8

The amount of bacteria in a Petri dish increases at a rate proportional to the amount present. At time t=0, the amount of bacter

ia in the dish is 10 grams. At time t=2, the amount of the bacteria in the dish is 30 grams. What is the amount of bacteria in the dish at time t=6?
A. 70 grams
B. 190 grams
C. 270 grams
D. 9270 grams
Mathematics
1 answer:
Len [333]2 years ago
8 0

Answer:

C. 270 grams

Step-by-step explanation:

-This is an exponential growth function which can be expressed using the formula:

P_t=P_oe^{rt}

Where:

  • P_t  is the size at time t.
  • P_o is the initial size
  • r is the growth rate
  • t is the time

Given the size at t=2 and at t=0, we substitute in the growth function to solve for r:

30=10e^{2r}\\\\3=e^{2r}\\\\r=\frac{In \ 3}{2}\\\\=0.54931

We use this calculated rate to determine the population at t=6

P_t=P_oe^{rt}\\\\=10e^{6\times \frac{In \ 3}{2}}\\\\=270\ grams

Hence, the bacteria's size at t=6 is 270 grams

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2 Classify the triangle by its sides. The diagram is not to scale. A straight B equilateral C scalene D isosceles (sides are 8,6
kow [346]

Answer:

D) Isosceles

Step-by-step explanation:

An isosceles triangle is the triangle that has 2 sides that are the same.

8 0
2 years ago
The CEO of Millennium Dairy Product, a small venture among 10 partners each having 100,000 shares, sought to raise an additional
klemol [59]

Answer:

Millennium Dairy Product

a) Share of the company that SBI Caps should require today to get a required rate of return of 50%.

= 50%

b) If the company had 1,000,000 (100,000 x10) shares outstanding before the private placement, SBI Caps should purchase

1,000,000 shares = 50% of (1,000,000 + 1,000,000) shares

Assuming the founding promoters are not giving up their shares, instead, new equity shares are being issued.

c) The price per share SBI Caps should agree to pay, if her required return was 50% is

Rs.50 per share, which will provide the required additional equity financing of (Rs.50 million) since Rs.50 x 1,000,000 equals Rs.50 million.

d) Pre money and post money valuations:

These are based on the calculated Market Price of Rs.1,000 per share from the Price/Earnings Ratio.

Pre money valuation will be Rs.1,000 x 1,000,000 shares = Rs.1 billion

Post money valuation will be Rs.1,000 x 2,000,000 shares = Rs.2 billion

e) Carried interests of the VC and the promoters

VC's carried interest = share of profits = 50% xRs.50 million = Rs.25 million

Promoters' carried interest = Rs.25 million

Step-by-step explanation:

a) Calculation of share in the company:

SBI Cap's required rate of return is 50%

If she invests Rs.50 million today, her expected return will be equal to Rs.50 million x 50% = Rs.25 million

Since rate of return = Net Income/Initial Investment or (Current value of investment - Initial Investment)/Initial Investment.

This return will be equal to 50% of the total net income of Rs.50 million

b) Price/Earnings P/E ratio = Market price per share/Earnings per share (EPS)

Since P/E ratio of similar companies = 20 times,

The company's P/E = 20 times x EPS

With calculated EPS = Rs.50 million /1,000,000 = Rs.50

Therefore, price per share = 20 x Rs.50 = Rs.1,000

Pre money valuation = Rs.1,000 x 1 million shares = Rs.1 billion

Post money valuation = Rs.1,000 x 2 million shares = Rs.2 billion

c) The carried interest is the share of profits to which the promoters and the Venture Capitalists are entitled.  Their respective shares are 50% of the net income = Rs.25 million each.

d) The pre money and post money valuations:  The pre money valuation is the valuation of the company before the additional equity financing.  The post money valuation is the valuation of the company after the additional equity financing.  There are many ways to value a company.  In this case, we have used the P/E ratio as a basis for the valuation.  However, we did not dilute the earnings per share post money, for simplicity.

3 0
2 years ago
Leicestershire Renovations has a history of problems with customers who do not pay their bills on time. Leicestershire Renovatio
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Complete Question.

Leicestershire Renovations has a history of problems with customers who do not pay their bills on time.

Leicestershire Renovations wants to improve its cash situation, reduce bad debts, and reduce credit-collection

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a. zone pricing

b. quantity discounts

c. cash discounts

d. by product pricing

e. product bundling

Answer:

c. Cash discounts.

Step-by-step explanation:

Cash discount is a reduction in the amount of an invoice allowed by some sellers of goods or service providers so as to encourage service takers or coients to pay within a specified period of time.

For the client or customer, it is known as the purchase discount while it is a sales discount for the service providers.

Cash discount will help Leicestershire Renovations improve its cash situation, reduce bad debts and reduce credit-collection

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Answer:

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-4x° = 144°

-x° = 144°/4

-x° = -36°

x° = 36°

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makkiz [27]
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2 years ago
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