SOLUTION: When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by {{{ Q(t)=Q[o](1-(e)^(-t/(a)))}}} (The m

Question 781452: When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by

(The maximum charge capacity is and t is measured in seconds.)
(a) Find the inverse of this function and explain its meaning.
(b) How long does it take to recharge a capacitor to 90% of capacity if
a = 2
I got
I would just really like to know if this equation is right because if it is then (b) should be about 4.6 seconds. Which is what I got.
Found 2 solutions by fcabanski, josgarithmetic:
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
You are right, but for this application you don't switch the variables. Only switch back for general finding inverse function. Q(t) is the charge at time t. It remains Q(t) for the inverse function.

where Q(t) is the amount of charge at time t, and is the original charge. The inverse function shows the time, t, needed to reach a certain % of original charge.
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
You found a correct form of the inverse of Q(t). Mine is equivalent to yours, expressed as .
I found y by simply switching places of t and Q(t), using y in place of Q(t), and solved for y.
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