Amanufacturer of electronic equipment requires a certain rare metal. he has a reserve supply of 4,000,000 units that he will not be able to replace. if the rate at which the metal is used is given by f(t)=100,000e.03t where t is time in years, how long will it be before he uses his supply?

This is the concept of algebra, we are required to get the time taken for the materials to be used up, given that the rate at which the metal is used is given by:
f(t)=100000e^(0,03t)
4000000=100000e^(0,03t
40=e^(0.03t)
introducing natural logs we get:
ln40=0.03t
thus;
t=(ln40)/0.03
t=122.96=123
The time taken before the material is used up will be 123