Lesson Plan

Isolate the exponential term in an equation of the form ab^(ct) = d by dividing both sides by a

Rewrite b^(ct) = d/a in logarithmic form as ct = log_b(d/a) for b = 2, 10, or e

Solve for the variable t by dividing both sides by c, obtaining t = log_b(d/a) / c

Evaluate logarithmic expressions using a calculator (log for base 10, ln for base e, and the change-of-base formula for base 2)

Interpret the solution in context (e.g., "the population reaches 1 million after approximately 14.2 years")

Apply the logarithmic solution method to real-world exponential models involving doubling time, half-life, and target-value problems

HSF.LE.A.4

HSF.LE.A.4: For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.