A function h(t) increases by 0.15 over every unit interval in t and h(0)=0.Which could be a function rule for h(t)?
Question
A function h(t) increases by 0.15 over every unit interval in t and h(0)=0.
Which could be a function rule for h(t)?
Solution
To derive the function rule for based on the provided information, let's analyze the details given:
-
Initial Value: The function starts at .
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Rate of Increase: The function increases by for each unit increase in .
Relevant Concepts
The general form for a linear function that describes the behavior over time can be expressed as:
Analysis and Detail
Given that and the function increases by for every unit increase in , the slope of the function can be determined as follows:
- Slope = 0.15
Now, substituting the values into the linear function formula:
Verify and Summarize
To verify, we can check a few values:
- When , (Correct)
- When , (Increases by 0.15)
- When , (Increases by another 0.15)
Final Answer
Thus, the function rule for is:
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