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Chapter 3: Problem 12

Estimate the indicated value without using a calculator. \(\frac{e^{5}}{e^{4.984}}\)

Short Answer

Expert verified
The estimated value of the expression \(\frac{e^{5}}{e^{4.984}}\) without using a calculator is approximately \(e^{0.016}\).

Step by step solution

01

Identify the base and exponents

In this case, the base is \(e\), and the exponents are \(5\) and \(4.984\).
02

Apply the rule of dividing exponents

Since both exponent expressions have the same base, we can apply the rule for dividing exponents: \[\frac{a^m}{a^n} = a^{m-n}\]. Applying the rule to our given expression, we get: \[\frac{e^5}{e^{4.984}}=e^{5-4.984}\].
03

Calculate the new exponent

We can estimate the difference between two numbers without a calculator by subtracting them: \[5-4.984 \approx 0.016\]. Note that this approximation is good enough for estimation purposes.
04

Express the final answer

By using the rule of dividing exponents and approximating the difference between the exponents, we obtain the simplified expression: \[e^{5-4.984} \approx e^{0.016}\]. This is the estimate of the indicated value without using a calculator.

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