A function h(t) increases by 1.45 over every unit interval in t and h(0)=5.Which could be a function rule for h(t)?

To find a function rule for $h(t)$, we can follow these steps:

1. Break Down the Problem

• We know that the function $h(t)$ increases by 1.45 for every unit increase in $t$.
• We also know that $h(0) = 5$.

2. Relevant Concepts

• A linear function can be expressed in the form $h(t) = mt + b$, where $m$ is the slope and $b$ is the y-intercept.
• In our case, the slope $m$ is 1.45, and the y-intercept $b$ is the initial value of the function when $t = 0$.

3. Analysis and Detail

• Since $h(0) = 5$, this means that when $t = 0$, the function's value is 5. This gives us the conditional point to establish the y-intercept.

• We can substitute these values into the linear function formula:

  $h(t) = 1.45t + 5$

4. Verify and Summarize

• If we plug $t = 0$ into the function:

  $h(0) = 1.45(0) + 5 = 5$

• For $t = 1$:

  $h(1) = 1.45(1) + 5 = 6.45$

• For $t = 2$:

  $h(2) = 1.45(2) + 5 = 7.90$

Thus, the function rule $h(t) = 1.45t + 5$ effectively meets all the criteria given in the problem.

Final Answer

The function rule for $h(t)$ is: $h(t) = 1.45t + 5$