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ludmilkaskok [199]
2 years ago
12

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

Mathematics
1 answer:
nalin [4]2 years ago
6 0

Answer:

156

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Functions
  • Function Notation
  • Average Rate of Change:  \displaystyle \displaystyle \frac{f(b) - f(a)}{b - a}

Step-by-step explanation:

<u>Step 1; Define</u>

<em>Identify</em>

f(x) = 5ˣ + 1

Interval <em>x</em> [0, 4] →<em>b</em> = 4, <em>a</em> = 0

<u>Step 2: Find Rate of Change</u>

  1. Substitute in variables [Average Rate of Change]:                                        \displaystyle \displaystyle \frac{f(4) - f(0)}{4 - 0}
  2. [Average Rate of Change] Substitute in <em>x</em> [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
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