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)
The value of e 2.1 calculated and rounded to three decimal places is approximately 8.166 . Using a calculator, you find the more precise value before rounding. This approximation is important in various mathematical applications.
;
Calculate e 2.1 using a calculator.
Round the result to three decimal places.
The approximation of e 2.1 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 the Result Rounding this value 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 important in these applications to make predictions and informed decisions.
