What percentage is likely to be infected in week 4 if N(3) = 8 and N′(3) = 1.2?

[bcahmel]

Homework Statement

Let N(t) be the percentage of a state population infected with a flu virus on week t of an epidemic. What percentage is likely to be infected in week 4 if N(3) = 8 and N′(3) = 1.2?

Homework Equations

Derivative EQs?

The Attempt at a Solution

My first(and failed) idea was t^3, since 2^3=8. but then this derivative didn't equal 1.2. I couldn't get the answer with my guess and check method...So is there another way I could try it?

 

[HallsofIvy]

You do understand that the derivative is a "rate of change" don't you? If the number of infected in week three was 8 and was increasing by 1.2 per week, how many do you think will be infected in one more week?

That is exactly the same as using the "tangent line" approximatin: Y(t)= N'(3)(t- 3)+ N(3).

 

[bcahmel]

thank you so much, I don't know why I didnt think of that!