In 2002 Home depos saes amounted to 58200000000. In 2006, its sales were 90800000000.
a. Write Home Depo's 2002 sales and 2006 sales in scientific notation.
b. What was the percent growth in Home Depo's sales from 200 to 2006? Do all work by using scientific notation.
2002 Sales: 5.82*10^10
2006 Sales: 9.08*10^10
Sales growth factor per year = (9.08)/5.82)^(0.25)
= 1.1176
The annual growth = 11.76%
a. To write Home Depo's 2002 sales and 2006 sales in scientific notation, we need to express the numbers in a format that includes a coefficient and a power of 10.
2002 sales: 58200000000 = 5.82 × 10^10
2006 sales: 90800000000 = 9.08 × 10^10
So, the 2002 sales in scientific notation is 5.82 × 10^10 and the 2006 sales in scientific notation is 9.08 × 10^10.
b. To find the percent growth in Home Depo's sales from 2002 to 2006, we need to calculate the percentage increase.
First, we need to find the difference between the sales in 2006 (9.08 × 10^10) and the sales in 2002 (5.82 × 10^10):
Difference = 9.08 × 10^10 - 5.82 × 10^10 = 3.26 × 10^10
Next, we calculate the percent growth using the formula:
Percent growth = (Difference / Initial value) × 100
Initial value = 5.82 × 10^10
Percent growth = (3.26 × 10^10 / 5.82 × 10^10) × 100
To divide the exponential numbers, we subtract the exponents:
Percent growth = (3.26 / 5.82) × 10^(10 - 10) × 100
Simplifying:
Percent growth = 0.5598 × 10^0 × 100
Since 10^0 is just 1, we have:
Percent growth = 0.5598 × 1 × 100
Percent growth = 55.98%
Therefore, the percent growth in Home Depo's sales from 2002 to 2006 is 55.98% (rounded to two decimal places).