#### To determine

**To find:**

We have to find the inverse of the function Q.

#### Answer

The inverse of the function Q is

Q-1t=-aln1-QQ0

#### Explanation

**Calculation:**

When a camera flash goes off, the bacteria immediately begin to recharge the flash’s

capacitor. The electric charge is given by

Qt=Q01-e-ta

Where, Q0 is maximum charge capacity and *t* is measured in seconds.

First, we write the function as

Q=Qt=Q01-e-ta

Now, we solve this equation for *t*

QQ0=1-e-ta

Or e-ta=1-QQ0=Q0-QQ0

Then, taking natural logarithmic on both sides, we have

-ta=lnQ0-QQ0

Or

-ta=ln1-QQ0

t=-aln1-QQ0

**Conclusion:**

The inverse of the function Q is

Q-1t=-aln1-QQ0

#### To determine

**To find:**

We have to find the time, which the batteries take to recharge the capacitor to 90% of capacity if

*a=2.*

#### Answer

Time taken by batteries to recharge the capacitor up to 90% is 4.60 seconds.

#### Explanation

**Calculation:**

The maximum capacity of the capacitor is Q0 and *a=2.* So, if it takes t time to recharge the capacitor to 90% of capacity Q0. So,

QQ0=90100

So,

t=-aln1-QQ0

=-2ln1-0.9

≈4.60

Thus, it takes approx. 4.60 seconds to recharge the capacitor to 90%.

**Conclusion:**

Time taken by batteries to recharge the capacitor up to 90% is 4.60 seconds.