if the person leaves the money in the bank, the time it will take for it to reach the given final amount is 6.3 years.
<h3>What is an interest in banking?</h3>
Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.
The formular for calculating compound interest is expressed as;
A = P(1 + r/n)^(n*t)
Where A is final amount, P is initial principal balance, r is interest rate, n is number of times interest applied per time period and t is number of time periods elapsed.
Given the data in the question;
- Initial principal balance P = $4000
- Interest rate r = 5.5% anuually = 5.5/100 = 0.055
- Final amount A = $5600
- Time t = ?
We substitute our given values into the expression above.
A = P(1 + r/n)^(n*t)
5600 = 4000(1 + 0.055/1)^(1*t)
5600 = 4000( 1.055 )^t
( 1.055 )^t = 5600 / 4000
( 1.055 )^t = 1.4
We take log of each sides
0.02325t = 0.1461
t = 0.1461 / 0.02325
t = 6.3
Therefore, if the person leaves the money in the bank, the time it will take for it to reach the given final amount is 6.3 years.
Learn more about compound interest here: brainly.com/question/27128740
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How many numbers do u need
Answer: the father is 44 years old now
Step-by-step explanation:
Let Bob's present age be represented by x
Let his father's present age be represented by y
Bob's age is 15 years less than half his father's age. This means that
x = y/2 - 15
x + 15 = y/2
y = 2x + 30
y - 2x = 30 - - - - - - - - - -1
In six years his father's age will be eleven years more than triple Bob's age. This means that
y + 6 = 3(x + 6) + 11
y + 6 = 3x + 18 + 11
y - 3x = 18 + 11 - 6
y - 3x = 18 + 11 - 6
y - 3x = 23 - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
x = 7
y = 2x + 30
y = 2×7 + 30
y = 14 + 30
y = 44
<h3>
Answer: (x+1)(x+3)</h3>
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Explanation:
Let's assume it factors into (x+a)(x+b)
The goal is to find the two numbers a and b.
FOIL out (x+a)(x+b) to get x^2+(a+b)x+ab
Note how a+b is the middle term and ab is the last term.
In the original expression, 4 is the middle term and 3 is the last term.
So we need to find two numbers that
There are two ways to multiply to 3 and they are
- 1 times 3 = 3
- -1 times -3 = -3
But only the first way has the factors add to 4. So that means a = 1 and b = 3.
Therefore (x+a)(x+b) = (x+1)(x+3)
And x^2+4x+3 = (x+1)(x+3)
9514 1404 393
Answer:
4) 6x
5) 2x +3
Step-by-step explanation:
We can work both these problems at once by finding an applicable rule.
where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.
This can be referred to as the <em>power rule</em>.
Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:
lim[h→0](f(x+h)-f(x))/h = 2ax +b
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4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.
5. The gradient of x^2 +3x +1 is 2x +3.
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If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.
