#### 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*