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kobusy [5.1K]
3 years ago
10

What is the exact time t, in years, needed for the balance of an account that earns 5% annual 8. Interest compounded continuousl

y to triple?
Mathematics
1 answer:
Brums [2.3K]3 years ago
3 0

Answer:

It takes 22.52 years for the balance to triple in value.

Step-by-step explanation:

Continuous compounding:

The amount of money earned using continuous compounding is given by the following equation:

A(t) = A(0)(1+r)^t

In which A(0) is the initial amount of money and r is the interest rate, as a decimal.

Interest rate of 5%.

This means that r = 0.05, and thus:

A(t) = A(0)(1+r)^t

A(t) = A(0)(1+0.05)^t

A(t) = A(0)(1.05)^t

Time for the balance to triple?

This is t for which A(t) = 3A(0). So

A(t) = A(0)(1.05)^t

3A(0) = A(0)(1.05)^t

(1.05)^t = 3

\log{(1.05)^t} = \log{3}

t\log{1.05} = \log{3}

t = \frac{\log{3}}{\log{1.05}}

t =  22.52

It takes 22.52 years for the balance to triple in value.

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Step-by-step explanation:

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A knife is three times the cost of a spoon. 9 spoons and 12 knifes cost ?82.80 workout the cost of 1 knife.
tankabanditka [31]

Let S = spoon

Let K = knife


1 knife is thee times the cost of a spoon, so it would be 3S

Now you have 9S + 12K = 82.80

We can replace the K with 3S:

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Simplify the left side:

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7 0
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Read 2 more answers
Which of the following is a solution of x^2+8x= -32
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Answer:

X1=-4+4i

X2=-4-4i

Step-by-step explanation:

X^2+8x+32=0

Δ=b^2-4ac=8^2-4(32)=-64<0

X1=(-b-i√Δ) /2a=(-8-8i)/2=-4-4i

X2=(-b+i√Δ) /2a=(-8+8i)/2=-4+4i

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