Answer:
156
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Algebra I
- Functions
- Function Notation
- Average Rate of Change: [tex]\displaystyle \displaystyle \frac{f(b) - f(a)}{b - a}[/tex]
Step-by-step explanation:
Step 1; Define
Identify
f(x) = 5ˣ + 1
Interval x [0, 4] →b = 4, a = 0
Step 2: Find Rate of Change
- Substitute in variables [Average Rate of Change]: [tex]\displaystyle \displaystyle \frac{f(4) - f(0)}{4 - 0}[/tex]
- [Average Rate of Change] Substitute in x [Function f(x)]: [tex]\displaystyle \displaystyle \frac{(5^4 + 1) - (5^0 + 1)}{4 - 0}[/tex]
- (Parenthesis) Evaluate exponents: [tex]\displaystyle \displaystyle \frac{(625 + 1) - (1 + 1)}{4 - 0}[/tex]
- (Parenthesis) Add: [tex]\displaystyle \displaystyle \frac{626 - 2}{4 - 0}[/tex]
- [Fraction] Subtract: [tex]\displaystyle \displaystyle \frac{624}{4}[/tex]
- Divide: [tex]\displaystyle \displaystyle 156[/tex]
