Let's analyze the data provided for sales over five months: [tex]\( \$1000, \$1050, \$1102.50, \$1157.63, \$1215.51 \)[/tex].
To determine if the sales increased linearly or exponentially, we'll calculate the percentage increase in sales from month to month.
The percentage increase from one month to the next is given by:
[tex]\[ \text{Percentage Increase} = \left( \frac{\text{Current Month's Sale} - \text{Previous Month's Sale}}{\text{Previous Month's Sale}} \right) \times 100 \][/tex]
1. Between Month 1 and Month 2:
[tex]\[ \text{Percentage Increase} = \left( \frac{1050 - 1000}{1000} \right) \times 100 = \left( \frac{50}{1000} \right) \times 100 = 5\% \][/tex]
2. Between Month 2 and Month 3:
[tex]\[ \text{Percentage Increase} = \left( \frac{1102.50 - 1050}{1050} \right) \times 100 = \left( \frac{52.50}{1050} \right) \times 100 \approx 5\% \][/tex]
3. Between Month 3 and Month 4:
[tex]\[ \text{Percentage Increase} = \left( \frac{1157.63 - 1102.50}{1102.50} \right) \times 100 = \left( \frac{55.13}{1102.50} \right) \times 100 \approx 5.00045\% \][/tex]
4. Between Month 4 and Month 5:
[tex]\[ \text{Percentage Increase} = \left( \frac{1215.51 - 1157.63}{1157.63} \right) \times 100 = \left( \frac{57.88}{1157.63} \right) \times 100 \approx 4.99987\% \][/tex]
Evaluating the calculated percentage increases: [tex]\( 5\%, 5\%, 5.00045\%, 4.99987\% \)[/tex], we can see that there is a very consistent increase in percentage terms.
Since these percentage increases are almost the same, it indicates a constant percentage increase in sales each month, which is a characteristic of exponential growth.
Therefore, analyzing the sales data and the consistent percentage increases, we conclude:
Exponentially, because the table shows a constant percentage increase in sales per month.
