Solving Inverse Functions in Electric Charge Equations

[Null_]

Homework Statement

1) When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by the following. (The maximum charge capacity is M and t is measured in seconds.)

Q(t) = M(1 - e-t/a)

(a) Find the inverse of this function and explain its meaning.


2. Let f(x) = 2 + x2 + tan(πx/2), where -1 < x < 1.
(a) Find f(f -1(4)).

Homework Equations

n/a

The Attempt at a Solution

(1) Q = M(1 - e^-t/a)
Q/M = 1 - e^-t/a
e^-t/a = 1 - Q/M
-t/a (ln e) = ln(1 - Q/M)
-t/a = ln(1 - Q/M)
t = -a[ln(1 - Q/M)]

That's not right.



(#2.) x = 2 + y^2 + tan(π*y/2)
4 = 2 + y^2 + tan(π*y/2)
*plug into wolfram alpha... y~0.642
f(x) = 2 + x2 + tan(πx/2) original formula
f(.642)= 2 + (.642^2) + tan (.642π/2)
f(.642)=2.4293


That's not right either.


I'm not really seeing where I went wrong in either of them..any help is appreciated.

 

[Mark44]

Homework Statement

1) When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by the following. (The maximum charge capacity is M and t is measured in seconds.)

Q(t) = M(1 - e-t/a)

(a) Find the inverse of this function and explain its meaning.


2. Let f(x) = 2 + x2 + tan(πx/2), where -1 < x < 1.
(a) Find f(f -1(4)).

Homework Equations

n/a

The Attempt at a Solution

(1) Q = M(1 - e^-t/a)
Q/M = 1 - e^-t/a
e^-t/a = 1 - Q/M
-t/a (ln e) = ln(1 - Q/M)
-t/a = ln(1 - Q/M)
t = -a[ln(1 - Q/M)]

Why do you think this is wrong? This is what I got, but I am uncertain about the equation you wrote. I think you meant Q = M(1 - e^(-t/a)). If that is what you meant, then your answer is correct. However, you did not explain the meaning of the inverse here.

That's not right.



(#2.) x = 2 + y^2 + tan(π*y/2)
4 = 2 + y^2 + tan(π*y/2)
*plug into wolfram alpha... y~0.642
f(x) = 2 + x2 + tan(πx/2) original formula
f(.642)= 2 + (.642^2) + tan (.642π/2)
f(.642)=2.4293


That's not right either.

Yes, you have an error here. You have the right idea, but probably made an error when you calculated f(.642). You should get a final answer that is close to 4. You'll get better results with more precision in your value for f^-1(4), which I took as 0.64216.

I'm not really seeing where I went wrong in either of them..any help is appreciated.

 

[Null_]

Why do you think this is wrong? This is what I got, but I am uncertain about the equation you wrote. I think you meant Q = M(1 - e^(-t/a)).
If that is what you meant, then your answer is correct. However, you did not explain the meaning of the inverse here.

I think it's wrong because it's an online homework assignment and it told me that my answer was wrong. :/ That is the right equation. Sorry, I got the explanation part right but just copied the whole question.

Yes, you have an error here. You have the right idea, but probably made an error when you calculated f(.642). You should get a final answer that is close to 4. You'll get better results with more precision in your value for f^-1(4), which I took as 0.64216.

Ah, gotcha. Thanks.