Use a calculator to approximate the exponential expression to 4 decimal places.
[tex]e^4[/tex]
[tex]e^4 \approx[/tex] $\square$ (Round to four decimal places as needed.)
Answer (1)
Calculate e 4 using a calculator.
Round the result to four decimal places.
The approximate value of e 4 is 54.5982 .
Explanation
Problem Analysis We are asked to approximate the value of e 4 to four decimal places. The number e is the base of the natural logarithm, and it's approximately equal to 2.71828. We need to calculate e 4 and round the result to four decimal places.
Calculating e^4 Using a calculator, we find that e 4 ≈ 54.598150033144236 .
Rounding to Four Decimal Places Rounding this value to four decimal places, we get 54.5982 .
Final Answer Therefore, e 4 ≈ 54.5982 .
Examples
Exponential expressions like e 4 are used in various fields, such as finance and physics. For example, in finance, continuously compounded interest is calculated using the formula A = P e r t , where A is the final amount, P is the principal, r is the interest rate, and t is the time. If you invest 1000 a t anin t eres t r a t eo f 5 A = 1000e^{0.05 \times 4} = 1000e^{0.2} \approx 1000 \times 1.2214 = 1221.40$. This shows how exponential expressions are used to model real-world phenomena.
