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So whenever we have exponential equations where we have bases that can’t be the same and we have variables in the exponents, what we have to do is use logarithms in order to get those exponents down to a level we can manipulate them. Let's do a couple of word problems dealing with exponential growth and decay.
So this first problem, suppose a radioactive substance decays at a rate of % per hour.
What percent of the substance is left after 6 hours? So let's make a little table here, to just imagine what's going on.
Exponential word problems almost always work off the growth / decay formula, A = Pe rt, where "A" is the ending amount of whatever you're dealing with (money, bacteria growing in a petri dish, radioactive decay of an element highlighting your X-ray), "P" is the beginning amount of that same "whatever", "r" is the growth or decay rate, and "t" is time.
If your class uses a textbook, choose a story problem from a recent chapter and invite students to come up and solve it. Mention to them that with their imaginations, they could write much better problems, and will do so in today's lesson.
Apr 08, · We'll again touch on systems of equations, inequalities, and functions but we'll also address exponential and logarithmic functions, logarithms, imaginary and . Identify the following as exponential decay, growth or neither: y=6 X (1/4)^x _____.