Question

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

Answer 1

Answer:

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:  $\displaystyle \displaystyle \frac{f(b) - f(a)}{b - a}$

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

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