Exponents

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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


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