Functions can be used to model real life scenarios
- The reasonable domain is .
- The average rate of change from t = 0 to 2 is 20 persons per week
- The instantaneous rate of change is .
- The slope of the tangent line at point (2,V(20) is 10
- The rate of infection at the maximum point is 8.79 people per week
The function is given as:
<u>(a) Sketch V(t)</u>
See attachment for the graph of
<u />
<u>(b) The reasonable domain</u>
t represents the number of weeks.
This means that: <em>t cannot be negative.</em>
So, the reasonable domain is:
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<u>(c) Average rate of change from t = 0 to 2</u>
This is calculated as:
So, we have:
Calculate <em>V(2) and V(0)</em>
So, we have:
Hence, the average rate of change from t = 0 to 2 is 20
<u>(d) The instantaneous rate of change using limits</u>
The instantaneous rate of change is calculated as:
So, we have:
Expand
Subtract V(t) from both sides
Substitute
Cancel out common terms
becomes
Limit h to 0
<u>(e) V(2) and V'(2)</u>
Substitute 2 for t in V(t) and V'(t)
So, we have:
<em>Interpretation</em>
V(2) means that, 20 people were infected after 2 weeks of the virus spread
V'(2) means that, the rate of infection of the virus after 2 weeks is 4 people per week
<u>(f) Sketch the tangent line at (2,V(2))</u>
See attachment for the tangent line
The slope of this line is:
The slope of the tangent line is 10
<u>(g) Estimate V(2.1)</u>
The <em>value of 2.1 </em>is
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<u>(h) The maximum number of people infected at the same time</u>
Using the graph, the maximum point on the graph is:
This means that:
The maximum number of people infected at the same time is approximately 21.
The rate of infection at this point is:
The rate of infection is <em>8.79 people per week</em>
Read more about graphs and functions at:
brainly.com/question/18806107