What is the average rate of change of the function f(x)=480(0.3)^x from x = 1 to x = 5?Enter your answer, as a decimal, in the box. Do not round your answer. __________________
Accepted Solution
A:
Answer:Average rate of change [tex]=-35.7084[/tex]Step-by-step explanation:Given function is [tex]f(x)=480(0.3)^x[/tex] and we need to find average rate of change of the function from [tex]x=1\ to\ x=5[/tex].Average rate of change [tex]=\frac{f(b)-f(a)}{b-a}[/tex]So,[tex]here\ b=5\ and\ a=1\\f(5)=480(0.3)^5\\=480\times0.00243=1.1664\\and\\f(1)=480(0.3)^1\\=480\times0.3=144[/tex]Average rate of change[tex]=\frac{f(b)-f(a)}{b-a}\\\\=\frac{f(5)-f(1)}{5-1}\\\\=\frac{1.1664-144}{5-1}\\\\=\frac{-142.8336}{4}= -35.7084[/tex]Hence, average rate of change of the function [tex]f(x)=480(0.3)^x[/tex] over the intervel [tex]x=1\ to\ x=5[/tex] is [tex]=-35.7084[/tex].