Pregunta
Find \( A \) in the equation below \[ A=13000\left(1+\frac{0.043}{2}\right)^{12} \]
Ask by Mathis Wyatt. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( A \) is approximately 16780.46.
Solución
Calculate or simplify the expression \( 13000*(1+0.043/2)^{12} \).
Calculate the value by following steps:
- step0: Calculate:
\(13000\left(1+\frac{0.043}{2}\right)^{12}\)
- step1: Divide the terms:
\(13000\left(1+\frac{43}{2000}\right)^{12}\)
- step2: Add the numbers:
\(13000\left(\frac{2043}{2000}\right)^{12}\)
- step3: Simplify:
\(13000\times \frac{2043^{12}}{2000^{12}}\)
- step4: Rewrite the expression:
\(1000\times 13\times \frac{2043^{12}}{2000^{12}}\)
- step5: Rewrite the expression:
\(1000\times 13\times \frac{2043^{12}}{1000^{12}\times 2^{12}}\)
- step6: Reduce the numbers:
\(13\times \frac{2043^{12}}{1000^{11}\times 2^{12}}\)
- step7: Multiply the fractions:
\(\frac{13\times 2043^{12}}{4096\times 1000^{11}}\)
The value of \( A \) in the equation \( A=13000\left(1+\frac{0.043}{2}\right)^{12} \) is approximately 16780.45776.
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar
Simplifique esta solución
Extra Insights
To solve for \( A \), we can start by simplifying the equation step by step. First, let's calculate \( \frac{0.043}{2} \): \[ \frac{0.043}{2} = 0.0215 \] Next, we substitute this back into the equation: \[ A = 13000\left(1 + 0.0215\right)^{12} \] \[ A = 13000\left(1.0215\right)^{12} \] Now we need to compute \( (1.0215)^{12} \): \[ (1.0215)^{12} \approx 1.268241 \] Now we multiply by 13000: \[ A \approx 13000 \times 1.268241 \approx 16485.13 \] Thus, the value of \( A \) is approximately \( 16485.13 \).
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium