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alexgriva
2 days ago
7

Sarah invested $2,500 in an account paying an interest rate of 2.1% compounded continuously. Assuming no deposits or withdrawals

are made, how much money, to the nearest hundred dollars, would be in the account after 14 years?
Mathematics
1 answer:
Svet_ta [11.3K]2 days ago
6 0

Response:

$3,000

Detailed breakdown:

This scenario is centered around compound interest, with the formula for compound interest defined as

Provided Data

A = final amount  =?

P = initial principal balance  = $2,500

r = interest rate = 2.1%= 0.021

t = number of time units passed= 14 years

By inserting our data into the compound interest equation, we can determine the final amount

A= 2500(1+0.021)^1^4\\A= 2500(1.021)^1^4\\A= 2500*1.3377\\A= 3344.25\\

Therefore, rounding to the nearest hundred gives us an account balance of $3,000

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If m abf=7b-24 and m Abe = 2b what is m EBF
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Since m∠abe = 2b, and angle abe consists of angles abf and ebf, we can write:
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What is the logarithm of the equilibrium constant, log K, at 25°C of the voltaic cell constructed from the following two half-re
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Answer:

4.0921 reflects the logarithm of the equilibrium constant.

Step-by-step explanation:

Fe^{2+} (aq) +2e^{-}\rightarrow Fe(s); ​E​° = - 0.41 V

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Iron has a negative reduction potential, indicating its tendency to lose electrons and undergo oxidation, and thus it will be at the anode.

E^{o}_{cell}=Reduction potential of cathode - Reduction potential of anode

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To determine the equilibrium constant, we utilize the correlation with Gibbs free energy, as follows:

\Delta G^o=-nfE^o_{cell}

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\Delta G^o=-RT\ln K_{eq}

Aligning these two equations yields:

nfE^o_{cell}=RT\ln K_{eq}

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n = electrons transferred = 2

F = Faraday's constant = 96500 C

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R = gas constant = 8.314 J/K.mol

T = reaction temperature = 25^oC=[273+25]=298K

Substituting values into the equation, we arrive at:

2\times 96500\times 1.21 V=8.314\times 298\times \ln K_{eq}

\ln K_{eq}=9.3478

\log K_{eq}=\frac{9.3478}{2.303}=4.0921

4.0921 represents the logarithm of the equilibrium constant.

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