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aliya0001 [1]
3 years ago
14

The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your

wine now, at a price of $P a bottle, or to sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of this wine t years from now is $P(1 + 20). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine?
Mathematics
1 answer:
Katyanochek1 [597]3 years ago
7 0

Answer: 64 years

Step-by-step explanation:

Let assume the dealer sold the bottle now for $P, then invested that money at 5% interest. The return would be:

R1 = P(1.05)^t,

This means that after t years, the dealer would have the total amount of:

$P×1.05^t.

If the dealer prefer to wait for t years from now to sell the bottle of wine, then he will get the return of:

R2 = $P(1 + 20).

The value of t which will make both returns equal, will be;

R1 = R2.

P×1.05^t = P(1+20)

P will cancel out

1.05^t = 21

Log both sides

Log1.05^t = Log21

tLog1.05 = Log21

t = Log21/Log1.05

t = 64 years

The best time to sell the wine is therefore 64years from now.

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Determine the factors of x2 − 12x − 20.
FrozenT [24]

Answer:

Step-by-step explanation:

Synthetic division is one way to determine whether or not a given number is a root of the quadratic.  x^2 − 12x − 20 can be rewritten as x^2 - 12x + 36 - 36 - 20, or (x - 6)^2 - 56, which does not have integer solutions:

(x - 6)^2 - 56 = 0 becomes (x - 6)^2 = 56, which works out to x - 6 = ± 2√14.

None of the possible roots suggested in this problem turns out to be an actual root.

correct response: PRIME

3 0
3 years ago
​You need to wrap a present that you will put inside a cylindrical container. You’ll need to know how much will fit in the conta
nirvana33 [79]

Answer:

149.28 sq. inches

137.5 cubic inches.

Step-by-step explanation:

The cylindrical container has length or height (h) 7 inches and has a diameter of 5 inches i.e. radius (r) 2.5 inches.

Now, total surface area of the container = 2\pi r^{2} + 2\pi rh

= \frac{2 \times 22 \times (2.5)^{2} }{7} + \frac{2 \times 22 \times 2.5 \times 7}{7}

= 39.28 + 110  

= 149.28 sq. inches (Answer)

Again the volume of the container will be \pi r^{2}h

= \frac{22 \times (2.5)^{2} \times 7}{7}

= 137.5 cubic inches. (Answer)

6 0
3 years ago
A new shopping mall is gaining in popularity every day since it open the number of shoppers is 20% more than the numbers of shop
erastovalidia [21]

Answer: the number of shoppers on the first day is 125

Step-by-step explanation:

The number of shoppers is 20% more than the numbers of shoppers the day before. It means that the number of shoppers is increasing in geometric progression. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

r = 1 + 20/100 = 1.2

n = 4(first 4 days)

S4 = 671

Therefore, the expression for the first 4 days is

671 = (a × 1.2^(4) - 1)/1.2 - 1

671 = (a × 1.2^(4) - 1)/0.2

671 = 1.0736a/0.2

671 = 5.368a

a = 671/5.368

a = 125

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2 years ago
Does1/3 & 7/21 form a proportion
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Because 1 * 21 = 3 * 7 ( 21  = 21 ) , 1/3&7/21 form a proportion.
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