16,080exp(0.002996 + 0 – 0.011)(3/12)

asked by guest
on Nov 15, 2024 at 2:54 pm



You asked:

Evaluate the expression: \(16,080 \cdot {e}^{0.002996 + 0 - 0.011} \cdot \frac{3}{12}\)

MathBot Answer:

\[16,080 \cdot {e}^{0.002996 + 0 - 0.011} \cdot \frac{3}{12} = \frac{4020}{e^{\frac{2001}{250000}}} \approx 3987.95234580369685787421422992913166\]

\[\begin{aligned}16,080 \cdot {e}^{0.002996 + 0 - 0.011} \cdot \frac{3}{12}& = 16080 \cdot e^{\frac{2996}{1000000} + 0 - \frac{11}{1000}} \cdot \frac{3}{12}\\& = 16080 \cdot e^{\frac{749}{250000} + 0 - \frac{11}{1000}} \cdot \frac{3}{12}\\& = 16080 \cdot e^{\frac{749}{250000} - \frac{11}{1000}} \cdot \frac{3}{12}\\& = 16080 \cdot \frac{1}{e^{\frac{2001}{250000}}} \cdot \frac{3}{12}\\& = 16080 \cdot e^{- \frac{2001}{250000}} \cdot \frac{3}{12}\\& = 4020 \cdot e^{- \frac{2001}{250000}}\end{aligned}\]

\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).

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