High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ What is the rate of decay, [tex] r [/tex] (expressed as a decimal), for data best modeled by the exponential function [tex] y = 63.4(0.92)^x [/tex]?

A. [tex] r = 36.6 [/tex]

B. [tex] r = 0.02 [/tex]

C. [tex] r = 0.08 [/tex]

D. [tex] r = 63.4 [/tex]

Answer :

To find the rate of decay, [tex]\( r \)[/tex], in the exponential function [tex]\( y = 63.4(0.92)^x \)[/tex], we should focus on the base of the exponential term, which is [tex]\( 0.92 \)[/tex].

In exponential decay models, the base of the exponent represents [tex]\( 1 - r \)[/tex], where [tex]\( r \)[/tex] is the rate of decay expressed as a decimal. Therefore, we can find [tex]\( r \)[/tex] by calculating:

[tex]\[ r = 1 - \text{base} \][/tex]

For this particular exponential function, the base is [tex]\( 0.92 \)[/tex]. So, the rate of decay [tex]\( r \)[/tex] is calculated as follows:

[tex]\[ r = 1 - 0.92 \][/tex]

[tex]\[ r = 0.08 \][/tex]

Therefore, the rate of decay, [tex]\( r \)[/tex], expressed as a decimal is [tex]\( \boxed{0.08} \)[/tex]. This matches one of the given options.