#### Answer

(a) $a = 100.0120124369$ and $b = 4.5149533\times 10^{-5}$ or $ 0.000045145933$
(b) -670 micro-amperes

#### Work Step by Step

(a) Follow some important steps while using T1-83 calculator.
1. Press STAT to view the statistics calculations or editing options.
2. Press the number associated with an option or uses the cursor keys to select an option.
3. Press enter and press 1 to select editing option which displays the lists of data.
4. Press 0 to select exponential regression which finds the best-fit exponential equation of the form as $y=ab^{x}$:
Therefore, the obtained model for $y=ab^{x}$ with $a = 100.0120124369$ and $b = 4.5149533\times 10^{-5}$ or $ 0.000045145933$
(b) 1. The working of flash unit on a camera operates on/off by storing charge on a capacitor and releasing it suddenly the flash is set off.
The data in the table describe the charge Q remaining on the capacitor at time t.
3. Use the data to draw the graph of this function and estimate the slope of the tangent line at the point where .
To calculate the current flowing from the capacitor to flash bulb, we will draw an approximation to the tangent line at P and measure the sides of the triangle ABC.
Using the given data
Slope of the tangent line at point
$I =\frac{Q}{t}=-|\frac{81.87-54.88}{0.06-0.02}|=-670$ micro-amperes