When Luis opened a mechanics shop, his total revenue, in thousands of dollars, was 2.1 in his first year. Each following year, his rate of growth of the total revenue has been 28%. Some of the revenue data for his shop is shown in the table.

Question

Year 1 2 3 4
Total Revenue

(In Thousands of Dollars)

2.1 2.688 3.44 4.04

Answer 1

To calculate the total revenue for each year, given a 28% growth rate, we can use the formula for annual growth:

\[ \text{Revenue}{n} = \text{Revenue}{n-1} \times (1 + r) \]

where \( r \) is the growth rate (in decimal form).

Starting with Year 1, we have:

• Year 1: Total Revenue = $2.1 (given)
• Year 2: \[ \text{Revenue}_2 = 2.1 \times (1 + 0.28) = 2.1 \times 1.28 = 2.688 \]
• Year 3: \[ \text{Revenue}_3 = 2.688 \times (1 + 0.28) = 2.688 \times 1.28 = 3.44 \]
• Year 4: \[ \text{Revenue}_4 = 3.44 \times (1 + 0.28) = 3.44 \times 1.28 = 4.4032 \approx 4.04 \text{ (rounded)} \]

So, the revenue growth for each year checks out:

• Year 1: $2.1
• Year 2: $2.688
• Year 3: $3.44
• Year 4: $4.04

If you need any further calculations or insights, feel free to ask!