Exponential functions

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Factoring

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MAT.116 4.1

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Exponential functions

simple interstate's and compound interest.

formulas

Compound interest- the interest you earn is based on the principal and the interest from the previous period.

compound interest example

Simple interest- the interest you earn is based only on the principal.

simple inters example

formula is. I=Prt

t- is the time in years

r- is the annual rate of interest (decimal)

P- is the principal

I is the simple interest

power of a power

examples of power to a power

when raising a power to another power the exponents get multiplied. (a^m)^n= a^m*n.

power and exponents

example of base, exponent and power

example

an expression that shows a base being multiplied by it self by the exponent number.

rational exponents

rational exponent

rational number- number that can be expressed as the quotient of two integers (fraction) where the divisor is not zero

monomial-algebra expression consisting of one term

another step by step example

example- 3xy^2

product and quotient rules-product is multiplying or adding exponents while quotient is to divide or subtract exponents.

dividing powers with the same base

answer is 4^2 which=16

multiplying powers with the same base and without

example without the same base. 3^2*4^1=9*4=36

example. 2^2*2^3= 2*2*2*2*2=2^5

Zero and negative exponents

negative exponents

any fractional base raised to a negative exponent is equal to the reciprocal of the base raised to the same positive exponent.

Subtopic

negative exponent example

rule. any base raised to a negative exponent is equal to reciprocal of the base raised to the same positive exponent. a^-m= 1/a^m

zero exponents

example of zero exponents

rule. any values except zero raised to the power of zero is equal to one. a^0=1