Question

In​ 1990, 28 % of bicycles in a certain country had tires wider than 25mm. Throughout the​ 1990s, this increased by approximately 0.6 % per year. If this trend​ continues, in which year will 61 % of bicycles in the country have tires wider than​ 25mm?
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Part 1
In
  
enter your response here​, 61 % of bicycles in the country will have tires wider than 25mm.

Answer 1

To determine when 61% of bicycles will have tires wider than 25mm, we can model the situation mathematically.

1. We start with the given information:
- In 1990, the percentage of bicycles with tires wider than 25mm was 28%.
- The percentage increases by approximately 0.6% each year.

2. Let \( P(t) \) represent the percentage of bicycles with tires wider than 25mm after \( t \) years from 1990. Thus, we can express this as:
\[
P(t) = 28\% + 0.6\% \cdot t
\]
where \( t = 0 \) corresponds to the year 1990.

3. We want to find \( t \) when \( P(t) = 61% \):
\[
28\% + 0.6\% \cdot t = 61\%
\]

4. Subtract 28% from both sides:
\[
0.6\% \cdot t = 61\% - 28\%
\]
\[
0.6\% \cdot t = 33\%
\]

5. Now, divide both sides by 0.6%:
\[
t = \frac{33\%}{0.6\%} = \frac{33}{0.6} = 55
\]

6. This tells us that it will take 55 years from 1990 for the percentage to reach 61%.

7. Therefore, we calculate the year:
\[
1990 + 55 = 2045
\]

**Conclusion:**
In **2045**, approximately 61% of bicycles in the country will have tires wider than 25mm.