Creating Exponential Equations ~Adapted from Walch
Education
Slide 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.
Slide 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.
Slide 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.
Slide 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.
Slide 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?
Slide 8
Create a list of known values y = 16 thats our final value b =
thats our rate (of decay) x = 3 rounds thats our time Using the
general form we see that our unknown value is a
Slide 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
Slide 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.
