Given the exponential function f(x) = 54(0.45)x, classify the function as exponential growth or decay and determine the percent rate of growth or decay. A.Exponential decay, 55% decrease B.Exponential growth, 45% increase C.Exponential decay, 45% decrease D.Exponential growth, 55% increase

Accepted Solution

Answer:Option A.Exponential decay, 55% decreaseStep-by-step explanation:we have[tex]f(x)=54(0.45)^{x}[/tex]This is a exponential function of the form[tex]f(x)=a(b)^{x}[/tex]wherea is the initial valueb is the baseb=(1+r)r is the rate of changeIn this problema=54b=0.45so0.45=1+rr=0.45-1r=-0.55Convert to percentager=-55% ------> is negative because is a exponential decay