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)?

To derive the function rule for $h(t)$ based on the provided information, let's analyze the details given:

1. Initial Value: The function $h(t)$ starts at $h(0) = 0$.

2. Rate of Increase: The function increases by $0.15$ for each unit increase in $t$.

Relevant Concepts

The general form for a linear function that describes the behavior over time can be expressed as: $h(t) = h(0) + \text{slope} \times t$

Analysis and Detail

Given that $h(0) = 0$ and the function increases by $0.15$ for every unit increase in $t$, the slope of the function can be determined as follows:

• Slope = 0.15

Now, substituting the values into the linear function formula: $h(t) = 0 + 0.15 \times t$ $h(t) = 0.15t$

Verify and Summarize

To verify, we can check a few values:

• When $t = 0$, $h(0) = 0.15 \cdot 0 = 0$ (Correct)
• When $t = 1$, $h(1) = 0.15 \cdot 1 = 0.15$ (Increases by 0.15)
• When $t = 2$, $h(2) = 0.15 \cdot 2 = 0.30$ (Increases by another 0.15)

Final Answer

Thus, the function rule for $h(t)$ is: $\boxed{h(t) = 0.15t}$