A2.5

Exponential and logarithmic functions and equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.

A2.5.ADetermine the effects on the key attributes on the graphs of f(x) = b^x and f(x) = log base b of x where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d.A2.5.BFormulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation.A2.5.CRewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations.A2.5.DSolve exponential equations of the form y = ab^x where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions.A2.5.EDetermine the reasonableness of a solution to a logarithmic equation.
Example Problems
A piece of machinery depreciates at a rate of per year. If the initial value is , what will it be worth after years?
A chemical sample decays at a rate of per day. If there are initially 250 mg, how much will remain after 7 days?
The battery capacity of a device decreases by each month. If the initial capacity is , what will it be after 18 months?
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