At the end of a year, a motor car company announces that sales of a pickup are down by 43% for the year. If sales continue to decrease by 43% in each succeeding year, how long will it take for sales to decrease to zero?

Options

A. 1 year
B. 2 year
C. 3 year
D. More than 5 years

Answer

To solve the problem of how long it will take for the sales of a pickup to decrease to zero when sales decrease by 43% each year, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- Let's assume the initial sales of the pickup trucks are 100 units.

2. **Calculating Sales After the First Year**:
- If sales decrease by 43%, then the remaining sales after the first year will be:
\[ \text{Sales after Year 1} = 100 - (43\% \text{ of } 100) = 100 - 43 = 57 \text{ units} \]

3. **Calculating Sales After the Second Year**:
- Now, we apply the same percentage decrease to the new sales figure:
\[ \text{Sales after Year 2} = 57 - (43\% \text{ of } 57) = 57 - 24.51 \approx 32.49 \text{ units} \]

4. **Calculating Sales After the Third Year**:
- Again, we apply the 43% decrease:
\[ \text{Sales after Year 3} = 32.49 - (43\% \text{ of } 32.49) = 32.49 - 13.95 \approx 18.54 \text{ units} \]

5. **Continuing the Process**:
- We can see that each year, the sales continue to decrease, but they will never actually reach zero. Instead, they will approach zero asymptotically.
- For example:
- Year 4: \( 18.54 - (43\% \text{ of } 18.54) \approx 10.54 \text{ units} \)
- Year 5: \( 10.54 - (43\% \text{ of } 10.54) \approx 6.00 \text{ units} \)
- Year 6: \( 6.00 - (43\% \text{ of } 6.00) \approx 3.42 \text{ units} \)

6. **Conclusion**:
- The sales will keep decreasing but will never actually reach zero. Therefore, it will take an infinite amount of time for the sales to decrease to exactly zero.