#### To determine

**a)**

**To find:**

The exponential model for the charge using calculator

**Solution:**Q=(100.012437)(0.000045)t

#### Explanation

Using scientific calculator we can fit the curve Q=abt using method of least squares

Q=abt

Taking natural logarithm on both sides

lnQ=lnabt=lna+lnbtlnQ=lna+tlnbY=A+BtWhere Y=lnQ,A=lna,B=lnb

To find the values of a,b the Normal Equations are

∑Y=nA+B∑t∑tY=A∑t+B∑t2

On solving we get

a=100.012437 and b=0.000045

**Conclusion:**

Q=(100.012437)(0.000045)t

**b)**

**To find:**

The derivative Q′(t) at t=0.04s

**Solution:**Q′(0.04)=−670.73μA

Given Q=abt

Differentiating, we get

Q′(t)=abtlnb

Q′(0.04)=(100.012437)(0.000045)0.04ln(0.000045)⇒Q′(0.04)=−670.73μA

On Comparing with example 1.4.2 Q′=−670μA, we see that the values are very close.

**Conclusion:**

Q′(0.04)=−670.73μA