2. Creating Exponential Equations ~Adapted from Walch Education

3. Key Concepts Exponential equations are equations that have the variable in the exponent. The general form of an exponential equation is y = a b x, where a is the initial value, b is the rate of decay or growth, and x is the time. The base, b, must always be greater than 0.

4. Also… Since the equation has an exponent, the value increases or decreases rapidly. If the b > 1, then the exponential equation represents exponential growth. If 0 < b < 1, then the exponential equation represents exponential decay.

5. You need to understand this: If the time is given in units other than 1 use the equation, where t is the time it takes for the base to repeat. Another form of exponential equation is y = a(1 ± r) t, where a is the initial value, r is the rate of growth or decay, and t is the time.

6. Creating Exponential Equations from Context 1.Read the problem statement first. 2.Reread the scenario and make a list or a table of the known quantities. 3.Read the statement again, identifying the unknown quantity or variable. 4.Create expressions and inequalities from the known quantities and variable(s). 5.Solve the problem. 6.Interpret the solution of the exponential equation in terms of the context of the problem.

7. Practice # 1 In sporting tournaments, teams are eliminated after they lose. The number of teams in the tournament then decreases by half with each round. If there are 16 teams left after 3 rounds, how many teams started out in the tournament?

8. Create a list of known values y = 16 that’s our final value b = that’s our rate (of decay) x = 3 rounds that’s our time Using the general form we see that our unknown value is a

9. Substitute the values and solve y = a b x The tournament started with 128 teams. Raise the base to the power of 3. Multiply by the reciprocal. a = 128

10. Practice # 2 A population of mice quadruples every 6 months. If a mouse nest started out with 2 mice, how many mice would there be after 2 years? Write an equation and then use it to solve the problem.

11. Thanks For Watching!!! ~Dr. Dambreville