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## #1 2006-02-20 02:22:26

DodgyPerson
Member
Registered: 2006-02-20
Posts: 3

### Car battery

Hey everyone. i have been having a problem with one question, hope u people can help me out.

Question: A 12 Volt car battery runs down to 1 volt and has to be recharged.

The formula for the voltage (volts) at any time t (hours) during charging is given by:

v = 12 - A (2^-t)

1) How can i find the value of A

2)Find the value of voltage after 6 hours.

3) The battery never reaches a full 12 volts recharge, but reaches a maximum charge of 11.9 volts. At what time in hours and minutes does this occur????

guys seriously need help, thank you.

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## #2 2006-02-20 02:34:47

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Car battery

Before you start charging, the battery is at 1 volt. At this point, the time is 0.

Plugging these values into the equation gives 1 = 12 - A (2^0) = 12 - A.
Therefore, A = 11.

Now that we know A, we can answer b).

At t=6, v = 12 - 11(2^-6) = 11.83V (2 decimal places)

For c), we know v and need to find t.

11.9 = 12 - 11(2^-t)
11(2^-t) = 0.1
2^-t = 0.0090909...
-t = log(2) 0.0090909... = -6.7813...
t = 6.7813... hours.

To convert the remainder into minutes, we multiply by 60.
0.7813... x 60 = 47 minutes, to the nearest minute.
Therefore, the total charging time is 6 hours, 47 minutes.

Why did the vector cross the road?
It wanted to be normal.

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