# Thread: re: solve exponential equations

1. ## re: solve exponential equations

Hi:
This is not really so urgent, but I couldn't find anywhere that exponential questions seem to go. Any tips?

Question is to solve the following:
The current, i amps, flowing through an electrical circuit at time t seconds is known to be decreasing according to the equation
i=Ie^(-5t)
where I is the current initially flowing. Given that the initial current in this circuit is 2 amps, calculate how long it takes for the current to decrease to 0.5 amps, giving your answer in seconds correct to 2 d.p.

hmmm!
current is decreasing from 2 to 0.5. So, it has decreased by 1.5.
Do I start here by - Ie^(-5t) becomes -5tIe - like in the basic logarithm rule
loga^n = nloga

If the initial current is 2, does this then become -5t2e?

2. Hello, morelemonzanybody?

The current, $i$ amps, flowing through an electrical circuit at time $t$ seconds
is known to be decreasing according to the equation . $i \:=\:Ie^{-5t}$
where $I$ is the current initially flowing.

Given that the initial current in this circuit is 2 amps,
calculate how long it takes for the current to decrease to 0.5 amps,

We are told the initial current is 2 amps.
. . So the function is: . $i \:=\:2e^{-5t}$

We are asked: When is $i = 0.5$ ?

We have: . $0.5 \:=\:2e^{-5t} \quad\Rightarrow\quad e^{5t} \:=\:4 \quad\Rightarrow\quad 5t \:=\:\ln 4$

Therefore: . $t \;=\;\frac{\ln4}{5} \;\approx\;0.28$ seconds.

3. ## re: thanks

I like your algebra. It's much simpler/more concise than some methods I have seen.
thank you.