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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The flash unit on a camera operates by storing charge on a capacitor and releasing i1 suddenly when the flash is set off. The following data describe the charge Q remaining on the capacitor (measured in microcoulombs, μC) at time t (measured in seconds).

t 0.00 0.02 0.04 0.06 0.08 0.10
Q 100.00 81.87 67.03 54.88 44.93 36.76

(a) Use a graphing calculator or computer to find an exponential model for the charge.

(b) The derivative Q′(t) represents the electric current (measured in microamperes, μA) Flowing from the capacitor to the flash bulb. Use part (a) to estimate the current when t = 0.04 s. Compare with the result of Example 2.1.2.

(a)

To determine

To find: The exponential model for the charge.

Explanation

Calculation:

Use the online graphing calculator and obtain the graph of an exponential model for the charge as shown below in Figure 1.

The exponential model is Q(t)=Q0ekt (1)

From given table t=0 and Q(0)=100 then substitute in equation (1),

Q(0)=Q0e0100=Q0

Substitute Q0=100 and from given table t=0.02 and Q(0.02)=81.87 in equation (1),

Q(0.02)=100ek(0.02)81.87=100e0.02k81

(b)

To determine

To estimate: The electric current when t=0.04s.

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