216x=36x+1 Write original equation.
(6³)x=(6²)x+1 Rewrite 216 & 36 as powers with base 6.
6³x=6²x+2 Multiply exponents.
3x=2x+2 Set exponents equal to each other.
x=2 Solve for x.
The solution is 2.
MM2A2Grade: 9,10,11,12 Description: MM2A2. Students will explore exponential functions. Elements:
a. Extend properties of exponents to include all integer exponents.
b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.
c. Graph functions as transformations of f(x) = a(x).
d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.
e. Understand and use basic exponential functions as models of real phenomena.
f. Understand and recognize geometric sequences as exponential functions with domains that are whole numbers.
g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.
(6³)x=(6²)x+1 Rewrite 216 & 36 as powers with base 6.
6³x=6²x+2 Multiply exponents.
3x=2x+2 Set exponents equal to each other.
x=2 Solve for x.
The solution is 2.
MM2A2Grade: 9,10,11,12 Description: MM2A2. Students will explore exponential functions. Elements:
a. Extend properties of exponents to include all integer exponents.
b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.
c. Graph functions as transformations of f(x) = a(x).
d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.
e. Understand and use basic exponential functions as models of real phenomena.
f. Understand and recognize geometric sequences as exponential functions with domains that are whole numbers.
g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.