To calculate the height $H$ of the winning pole vault 12 years after 1900, we use the given formula:

$H(t) = 0.01 \times t + 3.5$

where $t$ is the number of years since 1900. Plugging in $t = 12$:

$H(12) = 0.01 \times 12 + 3.5$

First, multiply $0.01 \times 12$:

$0.01 \times 12 = 0.12$

Then add 3.5:

$H(12) = 0.12 + 3.5 = 3.62 \text{ meters}$

So, the winning height 12 years after 1900 was 3.62 meters.

Would you like more details or have any questions about this calculation?

Here are 5 related questions:

1. What would the winning height be 50 years after 1900?
2. How would you calculate the year when the winning height reached 4 meters?
3. If the height formula changed to $H(t) = 0.02 \times t + 3.5$, how would the height in 12 years differ?
4. How does the model reflect the improvement in pole vaulting techniques over time?
5. What are some factors that could cause deviations from this linear model in actual Olympic results?

Tip: When dealing with formulas involving time, always double-check that the time variable $t$ is correctly interpreted, especially regarding the starting year.