Question

g(t)=−(t−1)^2+5

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

Answer 1

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

Step-by-step 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]:                     $\displaystyle \frac{[-(5 - 1)^2 + 5] - [-(-4 - 1)^2 + 5]}{5 + 4}$
2. (Parenthesis) Subtract:            $\displaystyle \frac{[-(4)^2 + 5] - [-(-5)^2 + 5]}{5 + 4}$
3. [Brackets] Exponents:             $\displaystyle \frac{[-16 + 5] - [-25 + 5]}{5 + 4}$
4. [Brackets] Add:                        $\displaystyle \frac{-11 - [-20]}{5 + 4}$
5. Distribute -1:                            $\displaystyle \frac{-11 + 20}{5 + 4}$
6. Add:                                         $\displaystyle \frac{9}{9}$
7. Divide:                                     $\displaystyle 1$