The rate of change of the function is -35.7
Step-by-step explanation:
The rate of change of a function [tex]f(x)[/tex] between two points [tex]x_1[/tex] and [tex]x_2[/tex] is given by the ratio between the increment of the function itself and the increment of the x-variable:
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
The function of this problem is
[tex]f(x)=480 (0.3)^x[/tex]
For [tex]x_1=1[/tex], the value of the function is
[tex]f(1)=480(0.3)^1=144[/tex]
For [tex]x_2=5[/tex], the value of the function is
[tex]f(5)=480(0.3)^5=1.2[/tex]
Therefore, the rate of change of the function is
[tex]m=\frac{f(5)-f(1)}{5-1}=\frac{1.2-144}{5-1}=-35.7[/tex]
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