Answer:
48
Step-by-step explanation:
We are given the exponential function:—
[tex]\displaystyle \large{f(x)=2^x+49}[/tex]
Finding average rate of change from x = 4 to x = 7:—
The formula to find average rate of change:—
[tex]\displaystyle \large{\frac{f(a)-f(b)}{a-b}}[/tex] or [tex]\displaystyle \large{\frac{f(x+h)-f(x)}{h}}[/tex]
Let a be 7 and b be 4, therefore:—
[tex]\displaystyle \large{\frac{f(7)-f(4)}{7-4} = \frac{(2^7+49)-(2^4+49)}{3}}[/tex]
Evaluate:—
[tex]\displaystyle \large{\frac{(128+49)-(16+49)}{3}}\\\displaystyle \large{\frac{128+49-16-49}{3}}\\\displaystyle \large{\frac{128+16}{3}}\\\displaystyle \large{\frac{144}{3}}\\\displaystyle \large{48}[/tex]
Therefore, the average of change from x = 4 to x = 7 is 48.
