Half Life Formula ~ Objective-C - objective-c

Question

Nt = N0e-λt
N0 is the initial quantity
Nt is the quantity that still remains after a time t,
t1/2 is the half-life
τ is the mean lifetime
λ is the decay constant
I am pretty stuck on how to make this into a formula for objective-c and I require it.
double sourceStart = [textField.text doubleValue];
double sourceNow = 0;
double daysBetween = 8;
if (textField.text.length > 0) {
//Find how many half lives have been accumulated
double totalNumberOfHalfLives = daysBetween / sourceHalfLife;
//Find the factor
double reductionFactor = pow(0.5, totalNumberOfHalfLives);
//Find the source strength now
double sourceNow = sourceStart * reductionFactor;
}
I'm assuming I need something a long the lines of this? or completely wrong.
Then, I also need to be able to find how many days have passed between a certain period of days, for instance. Start Date = Apr 15th Now Date = Apr 25th, 10 days between.. How do I work that out in objective c? As well as my original question.

Answer 1

This will do it (in straight C, but it'll work as-is in Objective-C, and you can extract the logic easily enough):
#include <stdio.h>
#include <math.h>
int main(void) {
double start_quantity = 100;
double half_life = 8;
double days = 16;
double end_quantity = start_quantity * pow(0.5, days / half_life);
printf("After %.1f days with a half life of %.1f days, %.1f decays to %.1f.\
n",
days, half_life, start_quantity, end_quantity);
return 0;
}
and outputs:
paul#local:~/src$ ./halflife
After 16.0 days with a half life of 8.0 days, 100.0 decays to 25.0.
paul#local:~/src$
For the second part of your question, you can store dates in an NSDate, and use the timeIntervalSinceDate: method to get the time between them in seconds. Something like this:
#import <Foundation/Foundation.h>
int main(int argc, const char * argv[])
{
#autoreleasepool {
const int kSecsInADay = 86400;
NSDate * startDate = [NSDate dateWithTimeIntervalSinceNow:-16 * kSecsInADay];
NSDate * endDate = [NSDate date];
NSTimeInterval seconds_diff = [endDate timeIntervalSinceDate:startDate];
double days_diff = seconds_diff / kSecsInADay;
NSLog(#"There are %.1f days between %# and %#.", days_diff,
[startDate description], [endDate description]);
}
return 0;
}
which outputs:
There are 16.0 days between 2014-04-09 21:41:12 +0000 and 2014-04-25 21:41:12 +0000.
Notes:
[NSDate date] returns an NSDate object representing the current time.
[NSDate dateWithTimeIntervalSinceNow:seconds] returns an NSDate object that's seconds seconds away from the current time. In this case, I've created it exactly 16 days before the current date. Based on the comments, in your case you'll also want to create startDate with [NSDate date], and then store it somewhere so you can calculate the difference between it and the current time at some point in the future.