Knowee
Questions
Features
Study Tools

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)?

🧐 Not the exact question you are looking for?Go ask a question

Solution

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

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

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

Relevant Concepts

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

Analysis and Detail

Given that h(0)=0 h(0) = 0 and the function increases by 0.15 0.15 for every unit increase in t 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×t h(t) = 0 + 0.15 \times t h(t)=0.15t h(t) = 0.15t

Verify and Summarize

To verify, we can check a few values:

  • When t=0 t = 0 , h(0)=0.150=0 h(0) = 0.15 \cdot 0 = 0 (Correct)
  • When t=1 t = 1 , h(1)=0.151=0.15 h(1) = 0.15 \cdot 1 = 0.15 (Increases by 0.15)
  • When t=2 t = 2 , h(2)=0.152=0.30 h(2) = 0.15 \cdot 2 = 0.30 (Increases by another 0.15)

Final Answer

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

This problem has been solved

Similar Questions

A function h(t) increases by a factor of 10 over every unit interval in t and h(0)=1.Which could be a function rule for h(t)?

A function f(t) increases by a factor of 9 over every unit interval in t and f(0)=1.Which could be a function rule for f(t)?

A function g(x) increases by a factor of 1.15 over every unit interval in x and g(0)=1.Which could be a function rule for g(x)?

A function g(t) decreases by a factor of 6 over every unit interval in t and g(0)=3.Which could be a function rule for g(t)?

A function f(x) increases by a factor of 1.9 over every unit interval in x and f(0)=2.Which could be a function rule for f(x)?

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.