Question

G(t)=−(t−1)^2+5

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

Answer 1

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`