Solving the Exponential Equation $(1.001)^{3321}$
The problem asks us to find the value of $(1.001)^{3321}$ given two other values involving the same base raised to different powers.
Key Exponent Property
We can use the exponent rule: $a^{m+n} = a^m \times a^n$.
Applying the Property
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Observe the relationship between the exponents: $1259 + 2062 = 3321$.
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Therefore, we can rewrite $(1.001)^{3321}$ using the exponent rule:
$ (1.001)^{3321} = (1.001)^{1259 + 2062} = (1.001)^{1259} \times (1.001)^{2062} $ -
Substitute the given values into the equation:
$ (1.001)^{3321} = 3.52 \times 7.85 $ -
Perform the multiplication:
$ 3.52 \times 7.85 = 27.632 $ -
The calculated value $27.632$ is approximately equal to the option $27.64$.
Final Answer Derivation
Based on the calculation using the exponent property $a^{m+n} = a^m \times a^n$, the value of $(1.001)^{3321}$ is found by multiplying the given values $(1.001)^{1259} = 3.52$ and $(1.001)^{2062} = 7.85$. The result is $3.52 \times 7.85 = 27.632$, which matches option 4.
Important Questions from Numerical Reasoning
If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aftercare’?
Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
If ROAD is written as URDG, then SWAN should be written as:
The head of newly formed government desires to appoint five of the six selected members P, Q, R, S, T and U to portfolios of Home, Power, Defense, Telecom and Finance. U does not want any portfolio if S gets one of the five. R wants either Home or finance or no portfolio. Q says that if S gets either power or Telecom, then she must get the other one. T insists on a portfolio if P gets one .
Which is the valid distribution of portfolios?The given question is followed by two statements; select the most appropriate option that solves the question. Capacity of a solution tank A is 70 % of the capacity of tank B. How many gallons of solution are in tank A and tank B?
Statements:
I) Tank A is 80% full and tank B is 40% full.
II) Tank A if full contains 14,000 gallons of solution.
