The mass, m grams, of a substance is increasing exponentially so that the mass at time t hours is m=250e^(0.021t). Find the time taken for the mass to double in value.

All exponential equations can be reduced to the form m=m₀e^kt, where m₀ is the initial mass. This means for our equation the initial mass is 250g. If the mass has doubled in size, then m now equals 2*250 = 500g. Plugging this into our exponential equation gives us 500=250e^0.021t , which we can then work through as follows to re-arrange for t:

e^0.021t = 500/250 = 2

0.021t = ln(2)

t = ln(2) / 0.021 = 33.0070086 = 33.0 hours (3 significant figures)