Approximate the number using a calculator.
[tex]e^{-0.47}[/tex]
[tex]e^{-0.47} \approx[/tex] $\square$ (Round to three decimal places.)
Answer (2)
The value of e − 0.47 is approximately 0.625 when rounded to three decimal places. This value is obtained by evaluating the exponential function and rounding the result appropriately.
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Calculate the value of e − 0.47 using a calculator: e − 0.47 ≈ 0.625002 .
Round the result to three decimal places.
The approximated value is 0.625 .
Explanation
Problem Analysis We are asked to approximate the value of e − 0.47 to three decimal places.
Calculating the Value Using a calculator, we find that e − 0.47 ≈ 0.6250022682827008 .
Rounding the Result Rounding this to three decimal places, we get 0.625 .
Final Answer Therefore, e − 0.47 ≈ 0.625 .
Examples
Exponential functions like e x are used to model various phenomena in real life, such as population growth, radioactive decay, and compound interest. For example, if you invest money in an account that pays continuous interest, the amount of money you have after a certain time is given by an exponential function. Approximating values of exponential functions is important in many applications.
