Question

James is contemplating an investment opportunity represented by the function A(t)=P(1.06)t, where P is the initial amount of the investment, and t is the time in years. If James invests $5000, what is the average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20?

Enter your answer as a number, like this: 42

Answer 1

Rate of change per year = $5300

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