To determine

To estimate:

The total amount of infection needed to develop symptoms of measles

Answer

7840

Explanation

1) Concept:

Area under the graph is

A=limn→∞∑i=1nfxi∆x

where,

∆x=b-an & xi=a+i∆x

2) Calculation:

The area under the graph of Nt from t=0 to t=12.

It is also given that there are six subintervals.

So take the interval 0, 12 with n=6

The function N has been modeled by function as

ft=-tt-21t+1

So find out  ∆x.

∆x=b-an=12-06=2

The total amount of infection needed to develop symptoms of measles is

A=∑i=16fxi∆x

=2f1+f3+f5+f7+f9+f11

Now find out the values of fxi.

f1=-11-211+1=40

f3=-33-213+1=216

f5=-55-215+1=480

f7=-77-217+1=784

f9=-99-219+1=1080

f11=-1111-2111+1=1320

Substitute all these values in above equation.

=240+216+480+784+1080+1320

=7840

Conclusion:

The total amount of infection needed to develop symptoms of measles is

7840 infectedcellsmL·days