Question 984015

first find {{{f(3)}}} and {{{f(4)}}}

{{{f(3) = -(5)^(3 -3) + 2}}}
{{{f(3) = -(5)^(0) + 2}}}

{{{f(3) = -1 + 2}}}
{{{f(3) =1}}}

so, first point is ({{{x[1]}}},{{{y[1]}}}= ({{{3}}},{{{1}}}

same way find second point

 {{{f(4)}}}

{{{f(4) = -(5)^(4 -3) + 2}}}
{{{f(4) = -(5)^(1) + 2}}}

{{{f(4) = -5 + 2}}}
{{{f(4) = -3}}}

so, second point is ({{{x[1]}}},{{{y[1]}}}= ({{{4}}},{{{-3}}})



 the average rate of change, or slope, is:

{{{(y[2]-y[1])/(x[2]-x[1])=(-3-1)/(4-3)=-4/1=-4}}}

so,the average rate of change from {{{x = 3}}} to {{{x = 4}}} is {{{highlight(-4)}}}