Students will use their knowledge of exponential functions of the form y = a(b)^(x/c) to solve exponential equations. The application problems require students to create a function to model the situation, then solve for either the value of the exponent, or the result of a given value of the exponent.
The use of negative exponents is necessary (for instance, to find when 1/8 = 1/2 ^ (x/2), they could use 2^ -3 = (2^ -2)^(x/2), to get -3=-2x/2 and solve for x)
The first 2 pages involve solving equations where students can manipulate the equations to have the "same base" to solve for the exponents as above. The final 4 pages have students using logs (or a graphing calculator if students have not learned about logs) to solve for the variable as the same base method is not possible. Students who do not yet know logs can complete this exercise, but solve for the answer using the intersection of curves on the graphing calculator. Quick instructions are included, and the document is editable to use this option.
6 pages of .doc word file plus 5 pages of pdf answers are included.
See Making Math Matter MMM for other calculus, precalculus and algebra application assignments and handouts.
Can be used as homework, handout, activity, worksheet or an assessment.