Question

F(x)=5^x+1 what’s the rate of change between x=0 and x=4

Answer 1

156

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Functions
• Function Notation
• Average Rate of Change:
  `\displaystyle \displaystyle (f(b) - f(a))/(b - a)`

Explanation:

Step 1; Define

Identify

f(x) = 5ˣ + 1

Interval x [0, 4] →b = 4, a = 0

Step 2: Find Rate of Change

1. Substitute in variables [Average Rate of Change]:
   `\displaystyle \displaystyle (f(4) - f(0))/(4 - 0)`
2. [Average Rate of Change] Substitute in x [Function f(x)]:
   `\displaystyle \displaystyle ((5^4 + 1) - (5^0 + 1))/(4 - 0)`
3. (Parenthesis) Evaluate exponents:
   `\displaystyle \displaystyle ((625 + 1) - (1 + 1))/(4 - 0)`
4. (Parenthesis) Add:
   `\displaystyle \displaystyle (626 - 2)/(4 - 0)`
5. [Fraction] Subtract:
   `\displaystyle \displaystyle (624)/(4)`
6. Divide:
   `\displaystyle \displaystyle 156`