the value y of an investment x months after the money was invested is given according to the equation. y =…
the value y of an investment x months after the money was invested is given according to the equation. y = 25,000(1.16)^(-x). as time goes on, does the value of the investment grow or decay? grow decay
Answer
Explanation:
Step1: Reescribir la ecuación
Podemos reescribir $y = 25000(1.16)^{-x}$ como $y=25000\left(\frac{1}{1.16}\right)^{x}$, ya que $a^{-n}=\frac{1}{a^{n}}$. Aquí, $\frac{1}{1.16}\approx0.862<1$.
Step2: Analizar el tipo de función
Para una función exponencial de la forma $y = a\cdot b^{x}$, si $0 < b< 1$, la función es de decay (decadencia). Como $\frac{1}{1.16}\approx0.862$ está entre 0 y 1, la función representa un decay.
Answer:
decay