Answer:
Rate of change per year = $5300
Step-by-step explanation:
Step 1: Substitute the variable P for the invested amount
1. A(t) = 5000(1.06)t
2. A(t) = (5300)t
Step 2: Substitute the variable t for the first 15 years
1. A(15) = (5300)(15)
2. A(15) = 79,500
Step 3: Substitute the variable t for the 20 years
1. A(20) = (5300)(20)
2. A(20) = 106,000
Step 4: Find your two ordered pairs and relation
First ordered pair: (15, 79,500)
Second ordered pair: (20, 106,000)
Relation: {(15, 79,500), (20, 106,000)}
Step 5: Find the slope or rate of change between 15 and 20 years
Let (y₁, x₁) = (15, 79,500)
Let (y₂, x₂) = (20, 106,000)
1. Use the slope expression: y₂ - y₁/x₂ - x₁
2. Substitute the correct values into the expression:
106,000 - 79,500/20 - 15
3. Simplify: 26500/5 = 5300
4. Hence, the rate of change in dollars per year is $5300
