Exponents
Euler's Number, e
A frequently used base in applications of exponential functions. It is an irrational number derived by finding what (1 + 1/x)^x as x approaches infinity
A = P(1+r/n)^nt
Formula for periodic compounding when compounding the interest at regular intervals (daily, weekly, monthly)
A = Pe^rt
Formula forwhen compounding the interest continuously
(₄√a)³ or ⁴√a³
How can fractional exponents be rewritten? Use a^¾ to answer.
Find the distance from the point to the asymptote (y=k). Apply the bafo to this distance. Then count from the asymptote.
How do you create an exponential function's graph when it has a bafo?
Apply (h,k) to the parent f(n) points. Find the distance from the point to the asymptote (y=k). Apply the bafo to this distance. Then count from the asymptote.
How do you create an exponential function's graph when it has both an (h, k) and a bafo?
1
If a base is raised to the power of 0, what will the answer always be?
The exponents will be multiplied
If a power and its base are being raised to another power, what will the result look like?
Multiply the numbers together
If the exponent is the same but the bases are different, what can you do?
The exponents will be subtracted
If two powers with the same base are divided, what will the quotient look like?
The exponents will be added
If two powers with the same base will be multiplied together, what will the product look like?
the denominator
If you have a negative exponent, where does it and its base belong?
-x
In the expression (-x)⁴, what is the base that will subsquently be raised to the fourth power?
x
In the expression -x⁴, what is the base that will subsquently be raised to the fourth power?
the product of n number of x's
In the expression xⁿ, what does the whole expression say?
the exponent
In the expression xⁿ, what is n called?
the base
In the expression xⁿ, what is x called?
6⁴
Solve: ((3)(2))⁴
8x³y³
Solve: (2xy)³
3⁵
Solve: (3²)(3³)
3⁸
Solve: (3⁴)²
x³y³
Solve: (xy)³
2x
Solve: 2xy⁰
3² = 9
Solve: 3⁴/3²
Natural exponential function
The function defined by f(x) = e^x
To indicate powers
What are exponents used for?
2.71828183
What is the approximate value of e?
4x³ means 4xxx, whereas (4x)³ means (4x)(4x)(4x)
What is the difference between 4x³ and (4x)³
y=k
What is the formula for an asymptote on an exponential graph?
If b^m = bⁿ, then m=n
What is true about exponential equations with the same base?
0<b<1
What will be the value of b if the graph shows exponential decay?
b>1
What will be the value of b if the graph shows exponential growth?
y = bⁿ (should be ^x) y = a・b^(x-h) +k
Write the parent function and general form for an exponential function