Pregunta
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. \[ y=8600(0.11)^{x} \] Answer Attempt sout of 2 Growth ~ \% increase Submit Answer
Ask by Salazar Franklin. in the United States
Feb 25,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The function y = 8600(0.11)^x represents exponential decay with an 89% decrease per unit increase in x.
Solución
The function is given by y = 8600(0.11)^x. Notice that the base of the exponential term is 0.11, which is less than 1. This tells us that as x increases, y gets multiplied by 0.11 each time, meaning the function represents exponential decay.
To find the percentage rate of decay:
• Subtract the base from 1: 1 − 0.11 = 0.89.
• Convert this to a percentage: 0.89 × 100% = 89%.
Thus, the function represents exponential decay with an 89% decrease per unit increase in x.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Extra Insights
This exponential function represents decay since the base, 0.11, is less than 1. In exponential decay, the value of \( y \) decreases as \( x \) increases. To determine the percentage rate of decrease, subtract the base from 1 and multiply by 100: \[ (1 - 0.11) \times 100 = 89\% \] Thus, the function indicates an 89% decrease. When looking at exponential functions more broadly, remember that growth functions will always have a base greater than 1 (like 1.1, which indicates a 10% growth). Conversely, bases between 0 and 1 will show decay, as in this case where you see the percentage drop. Recognizing this pattern can help dissect exponential behaviors in various scenarios!
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
