Question

(3 points) consider the equation $y = 4.81(e)^{-0.0745t}$, which is of the form $y = ae^{rt}$, to fill in the following blanks. the $r$ value for the equation is \boxed{}. therefore, the type of change represented is? because?. note: you can earn partial credit on this problem. preview my answers submit answers show me another you have attempted this problem 0 times. you have 5 attempts left before new version will be requested. you have unlimited attempts remaining. email instructor page generated at 11/29/2025 at 03:38pm cst webwork \\(\copyright\\) 1996-2023 | theme: math4 | ww_version: 2.18 | pg_version 2.18 the webwork project

Explanation:

Step1: Identify the form of the exponential function

The general form of an exponential function is \(y = Ae^{rt}\). In the given equation \(y = 4.81e^{- 0.0745t}\), we can directly compare the coefficients.

Step2: Determine the value of \(r\)

By comparing \(y = 4.81e^{- 0.0745t}\) with \(y = Ae^{rt}\), we can see that \(r=-0.0745\).

Step3: Determine the type of change

Since \(r=-0.0745<0\), the function represents exponential decay. The reason is that for the exponential function \(y = Ae^{rt}\), when \(r>0\) it is exponential growth and when \(r < 0\) it is exponential decay.

Answer:

The \(r\) value is \(-0.0745\). The type of change represented is exponential decay because \(r=-0.0745 < 0\).