Approximate the number using a calculator.
[tex]e^{2.1}[/tex]
[tex]e^{2.1} \approx[/tex] $\square$ (Round to three decimal places.)
Answer (2)
Calculate the value of e 2.1 , which is approximately 8.166169912567652 .
Round the result to three decimal places.
The approximation of e 2.1 rounded to three decimal places is 8.166 .
Explanation
Problem Analysis We are asked to approximate the value of e 2.1 and round the result to three decimal places.
Calculating the Value Using a calculator, we find that e 2.1 ≈ 8.166169912567652 .
Rounding to Three Decimal Places Rounding this result to three decimal places, we get 8.166 .
Final Answer Therefore, e 2.1 ≈ 8.166 .
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 earns continuously compounded interest, the amount of money you have after a certain time is given by an exponential function. Approximating values of exponential functions is crucial in finance, science, and engineering for making predictions and decisions.
The value of e 2.1 is approximately 8.166169912567652 , which rounds to 8.166 when rounded to three decimal places. Therefore, e 2.1 ≈ 8.166 .
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