Math Help - exponential function

1. exponential function

Given T(subscript1/2) to be .0247 seconds, how long should it take to reach 93.75% of maximum charge?

2. Originally Posted by karnold9
Given T(subscript1/2) to be .0247 seconds, how long should it take to reach 93.75% of maximum charge?
You are doing nobody any favours with this question, you have not provided enough context for anyone to answer without guessing what the question really is.

Lets assume that $T_{1/2}$ is the time to reach $1/2$ maximum charge from flat for a charging model where the rate of charging is proportional to the difference between the maximum charge and the current charge.

Then starting from zero charge the charge state at time $t$ is:

$\frac{C}{C_{mx}}= (1-e^{-kt})$

Then we solve for $k$ from:

$0.5= (1-e^{-k\times 0.247})$

Then having found $k$ we solve for $t$ is:

$0.9375= (1-e^{-kt})$

(the arithmetic is slightly easier if we write the charging law as:

$\frac{C}{C_{mx}}= (1-2^{-kt})$

which you can try if you like)

RonL