How to use variable in main function as input argument to sub function? ERROR: Exiting fzero: aborting search...

Hello! First a brief intro... My task is to first create a function that calculates the volume of a reservoir as a function of the consumption rate and time (both given). Then, I am supposed to use that function as a SUBFUNCTION as part of another function that will determine the time it takes for the volume to decrease to a certain percentage of the initial volume (percentage is also given).

The given volume function is :

V(r,t) = 10^9 - 10^8 * (1 - exp (-t/100)) - r*t

For testing purposes, I am using:

the consumption rate, r = 10^7 liters

the percentage, x = .50

The answer should be, t_drain = 54.2 days...

My plan was to

1. Create the main function that makes the percentage variable and rate variable global
2. Create a time array with increments of .4167 days (about 1 hour)
3. Create a sub function that calculates volume of the reservoir as a function of time
4. Use that time array as an input argument to the sub function
5. Have the sub function also calculate difference between the critical volume (when the volume of reservoir = percent of initial volume) and the volume at any time
6. Use fzero in the main function to determine at what time the volume had decreased to the percent of the initial volume

What I am having the most trouble understanding is how I can use the array of times I created, time, as an input argument for my sub function. I don't think I did it right.

Here is what I have so far:

function t_drain = DC (x, r)

global perc rate time
perc = x;
rate = r;

%Sets maximum time t.
t_max = 1000;

%Creates array of times with each interval being one hour
time = 0:0.4167:t_max;

function v_diff = diff (time)
    global t v_limit  
    t = time;

      %Calculates water volume as a function of consumption rate and time.
      v = 10^9 + 10^8 .* (1-exp(-t./100)) - rate.*t;

      %Calculates limit for water volume to reach x percent of initial 10^9 L.
      v_limit = perc * 10^9;

      %Calculates difference between final volume and volume at time t. 
      v_diff = v - v_limit;

end
t_drain = fzero (@diff, 50);

end

Running this with x = .50 and r = 10^7 I get the error:

Exiting fzero: aborting search for interval containing a sign change because NaN or Inf function value encountered during search. Function Value at -92631.9 is -Inf. Check function or try again with a different starting value.

ans = NaN

However, to make sure that my algebra/math wasn't wrong I did a command window session where I ran the sub function and was able to see where v_diff was zero so I am pretty confident in that actual expressions within the sub function, just not the input argument.

I appreciate any help. Thank you.