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G(t)=−(t−1)^2+5

What is the average rate of change of g over the interval -4≤t≤5?

User Pixy
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1 Answer

7 votes

Answer:

1

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

  • Average Rate of Change:
    \displaystyle (f(b) - f(a))/(b - a)

Explanation:

Step 1: Define

g(t) = -(t - 1)² + 5

-4 ≤ t ≤ 5

Step 2: Identify Variables

a = -4

b = 5

Step 3: Solve

  1. Substitute [ARC]:
    \displaystyle ([-(5 - 1)^2 + 5] - [-(-4 - 1)^2 + 5])/(5 + 4)
  2. (Parenthesis) Subtract:
    \displaystyle ([-(4)^2 + 5] - [-(-5)^2 + 5])/(5 + 4)
  3. [Brackets] Exponents:
    \displaystyle ([-16 + 5] - [-25 + 5])/(5 + 4)
  4. [Brackets] Add:
    \displaystyle (-11 - [-20])/(5 + 4)
  5. Distribute -1:
    \displaystyle (-11 + 20)/(5 + 4)
  6. Add:
    \displaystyle (9)/(9)
  7. Divide:
    \displaystyle 1
User Ed Prince
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