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The given equation for the beanstalk's height is:

\[
h(t) = 6 + 0.75t
\]

Here, \( h(t) \) represents the height of the beanstalk in inches after \( t \) days. The term \( 6 \) in the equation represents the initial height of the beanstalk (the height at \( t = 0 \)).

Thus, the beanstalk's initial height is **6 inches**.

The correct answer is: **6 inches**.

Would you like further explanation or have any other questions?

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Here are some related questions to expand your understanding:

1. What does the \( 0.75t \) term in the equation represent?
2. How would the beanstalk's height change after 10 days?
3. What is the growth rate of the beanstalk per day?
4. If the initial height were doubled, how would the equation change?
5. How long would it take for the beanstalk to reach 10 inches in height?

**Tip**: In linear equations like this, the constant term represents the starting value, and the coefficient of \( t \) represents the rate of change over time.

A beanstalk grows at a constant rate. The beanstalk’s height (inches) as a function of time (days) is modeled by h(t) = 6 + 0.75t. What is the beanstalk’s initial height?

This problem models the height of a beanstalk as a linear equation, h(t) = 6 + 0.75t, where 6 represents the initial height. Learn how to solve for the initial height and understand the rate of growth.

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