How To Solve Exponential Decay Problems

If we use the approximate rounded-off value for k we will compound the error by rounding off again at the end when calculating the final result.Example: During its exponential growth phase, a certain bacterium can grow from 5,000 cells to 12,000 cells in 10 hours.

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It is best to work from the inside out, starting with the exponent, then the exponential, and finally the multiplication, like this: Not all algebra classes cover this method.

If you're required to use the first method for every exercise of this type, then do so (in order to get the full points).

Half-life is the amount of time it takes for a substance to decay to half of the original amount.

Example: A certain isotope has a half-life of 4.2 days.

Note that the constant was positive, because it was a growth constant.

If I had come up with a negative answer, I would have known to check my work to find my error.Example: A certain bacterium has an exponential growth rate of 25% per day.If we start with 0.5 gram and provide unlimited resources how much bacteria can we grow in 2 weeks?Step 2: Substitute the initial amount and k to formulate a model. Example: During its exponential growth phase, a certain bacterium can grow from 5,000 cells to 12,000 cells in 10 hours.At this rate how many cells will be present after 36 hours? Tip: Use the exact value for k and avoid round-off error.(I might want to check this value quickly in my calculator, to make sure that this growth constant is positive, as it should be.If I have a negative value at this stage, I need to go back and check my work.), try to do the calculations completely within the calculator in order to avoid round-off error.At this rate how long will it take to grow to 50,000 cells? Example: A certain animal species can double its population every 30 years.Assuming exponential growth, how long will it take the population to grow from 40 specimens to 500? Up to this point, we have seen only exponential growth.How long will it take a 150-milligram sample to decay so that only 10 milligrams are left?Answer: It takes about 1,343.5 years for a bone to lose 15% of its carbon-14. Put together a mathematical model using the initial amount and the exponential rate of growth/decay.

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