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aksik [14]
3 years ago
13

The Johnson family wants to start a college fund for their daughter Gabriella. They put $63, 000 into an account that grows at a

rate of 2.55% per year, compounded quarterly. Given the function G(t)= 63,000(1+ .0255/4)^ 4t, where G(t) represents the amount of money in the account t years after the account is opened, given that no more money is deposited into or withdrawn from the account.
Calculate the number of years it will take for the account to reach approximately $150,000, to the nearest hundredth of a year.
Mathematics
1 answer:
Rainbow [258]3 years ago
5 0

Answer:

<em>It will take approximately 34.13 years</em>

Step-by-step explanation:

The function G(t) below represents the amount of money in some account t years after the account is opened for The Johnson's daughter Gabriella:

G(t)= 63,000(1+ .0255/4)^ {4t}

It's required to find the number of years (t) it will take for the account to reach G(t)=150,000. We need to solve the equation:

63,000(1+ .0255/4)^ {4t}=150,000

Dividing by 63,000 and simplifying:

\displaystyle (1+ .0255/4)^ {4t}=\frac{150,000}{63,000}=2.38095

Taking logarithms:

\displaystyle \log(1+ .0255/4)^ {4t}=\log 2.38095

Applying logarithms property:

\displaystyle (4t) \log(1+ .0255/4)=\log 2.38095

Solving for t:

\displaystyle 4t =\frac{\log 2.38095}{\log(1+ .0255/4)}

\displaystyle t =\frac{\log 2.38095}{4\log(1+ .0255/4)}

Calculating:

\displaystyle t =\frac{0.37675}{0.01104}

\boxed{t \approx 34.13}

It will take approximately 34.13 years

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yuradex [85]

Answer:

splitting it evenly among all three sides gives us the greatest area. ( for example if we had to split the number 10 into 2 and find the greatest area, out of all possible ways 5*5 is the greatest). Two sides have to be equal since it's a rectangle.

918/3=306

So we can make the two equal sides 306, and the longer side 308 which makes sure that we have the greatest area.

306 * 308

Step-by-step explanation:

3 0
3 years ago
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3 years ago
Nemecek Brothers make a single product on two separate production lines, A and B. Its labor force is equivalent to 1000 hours pe
frez [133]

Answer:

(a) The inequality for the number of items, x, produced by the labor, is given as follows;

250 ≤ x ≤ 600

(b) The inequality for the cost, C is $1,000 ≤ C ≤ $3,000

Step-by-step explanation:

The total time available for production = 1000 hours per week

The time it takes to produce an item on line A = 1 hour

The time it takes to produce an item on line B = 4 hour

Therefore, with both lines working simultaneously, the time it takes to produce 5 items = 4 hours

The number of items produced per the weekly labor = 1000/4 × 5 = 1,250 items

The minimum number of items that can be produced is when only line B is working which produces 1 item per 4 hours, with the weekly number of items = 1000/4 × 1 = 250 items

Therefore, the number of items, x, produced per week with the available labor is given as follows;

250 ≤ x ≤ 1250

Which is revised to 250 ≤ x ≤ 600 as shown in the following answer

(b) The cost of producing a single item on line A = $5

The cost of producing a single item on line B = $4

The total available amount for operating cost = $3,000

Therefore, given that we can have either one item each from lines A and B with a total possible item

When the minimum number of possible items is produced by line B, we have;

Cost = 250 × 4 = $1,000

When the maximum number of items possible, 1,250, is produced, whereby we have 250 items produced from line B and 1,000 items produced from line A, the total cost becomes;

Total cost = 250 × 4 + 1000 × 5 = 6,000

Whereby available weekly outlay = $3000, the maximum that can be produced from line A alone is therefore;

$3,000/$5 = 600 items = The maximum number of items that can be produced

The inequality for the cost, C, becomes;

$1,000 ≤ C ≤ $3,000

The time to produce the maximum 600 items on line A alone is given as follows;

1 hour/item × 600 items = 600 hours

The inequality for the number of items, x, produced by the labor, is therefore, given as follows;

250 ≤ x ≤ 600

8 0
3 years ago
How many lb of brand X sugar which
Dafna1 [17]

Answer:  <u>4 pounds</u> of brand X sugar

====================================================

Reason:

n = number of pounds of brand X sugar

5n = cost of buying those n pounds, at $5 per pound

Brand Y costs $2 per pound, and you buy 8 lbs of it, so that's another 2*8 = 16 dollars.

5n+16 = total cost of brand X and brand Y combined

n+8 = total amount of sugar bought, in pounds

3(n+8) = total cost because we buy n+8 pounds at $3 per pound

The 5n+16 and 3(n+8) represent the same total cost.

Set them equal to each other. Solve for n.

5n+16 = 3(n+8)

5n+16 = 3n+24

5n-3n = 24-16

2n = 8

n = 8/2

n = 4 pounds of brand X sugar are needed

-------------

Check:

n = 4

5n = 5*4 = 20 dollars spent on brand X alone

16 dollars spent on brand Y mentioned earlier

20+16 = 36 dollars spent total

n+8 = 4+8 = 12 pounds of both types of sugar brands combined

3*12 = 36 dollars spent on both types of sugar brands

The answer is confirmed.

--------------

Another way to verify:

5n+16 = 3(n+8)

5*4+16 = 3(4+8)

20+16 = 3(12)

36 = 36

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olya-2409 [2.1K]

Answer:

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Step-by-step explanation:

distribute the 6 to 6, 6, and 2v.

36 + 36 + 12v=

12v + 72

8 0
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