[tex]f(a+199)=85.742[/tex]
Step-by-step explanation:
Here we have , Suppose f ( a ) = 64.25 and the average rate of change of f over the interval from x = a to x = a + 199 is 0.108. We need to What is the value of f ( a + 199 ) . Let's find out:
Rate of change of a function in interval [a,b] is given by:
⇒ [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here we have the following according to info given in question ,
⇒ [tex]\frac{f(a+199)-f(a)}{(a+199)-a} = 0.108[/tex]
⇒ [tex]\frac{f(a+199)-64.25}{199} = 0.108[/tex]
⇒ [tex](199)\frac{f(a+199)-64.25}{199} = 0.108(199)[/tex]
⇒ [tex]f(a+199)-64.25 =21.492[/tex]
⇒ [tex]f(a+199)=64.25 +21.492[/tex]
⇒ [tex]f(a+199)=85.742[/tex]
Therefore , [tex]f(a+199)=85.742[/tex] .
