Exponential Learned

Exponential relationships and models EXPONENTIAL REALTIONSHIP Exponential relationships describe a specific pattern of change between a dependent and independent variable EXPONENTIAL AND LINEAR

Linear equation- Y=MX+B X=slope B=y intercept Exponential Equation-Y=A *Bx Where A is the initial value and B is the growth factor Ex. On the first day, I went to one person’s house. On the second day, I went to 2 peoples homes. On the third day, I went to four peoples homes. The exponential equation for this word problem would be, for the initial value, 1 because the first day I stayed at 1 persons house, and for the growth factor, 2 because the number of people house that I went to was doubling.

Exponential growth-When the growth factor is above 1 Which of these equations contain/contains exponential growth? A) Y=2 * 0.67x B) Y=45 * 7.45x C) Y=6.3 * 6.67x Answer: B and C This is because you can see that both growth factors are above 1 Exponential Decay -if the growth factor is a number less than one Which of these equations contain/contains exponential decay? A) Y=2 * 0.67x B) Y=45 * 7.45x C) Y=6.3 * 6.67x Answer: A This is because you can see that the growth factor is below 1 If you bounce a ball a few times and calculate the height of the bounce you’ll notice that the height of one bounce is smaller than the height the previous one. This is called exponential decay because each bounce has a smaller height than its previous one. Growth FactorWhich of these equations contain/contains a growth factor? A) Y= 53x + 62 B) Y=45 * 7.45x C)Y =6.3x - 4 Answer: B This is because you can see that B is the only one that is an exponential equation, so it must be the only one with a growth factor Ratio- the relationship between two quantities Jeannine has a bag with 3 videocassettes, 4 marbles, 7 books, and 1 orange.

1) What is the ratio of books to marbles? Expressed as a fraction, with the numerator equal to the first quantity and the denominator equal to the second, the answer would be 7/4. Two other ways of writing the ratio are 7 to 4, and 7:4. 2) What is the ratio of videocassettes to the total number of items in the bag? There are 3 videocassettes, and 3 + 4 + 7 + 1 = 15 items total. The answer can be expressed as 3/15, 3 to 15, or 3:15.

Variable- a quantity or function that may assume any given value or set of values Age can be considered a variable because age can change value at different times. Similarly, country can be considered a variable because a person’s country can change if they move Exponent- a symbol or number placed above and after another symbol or number to denote the power to which the latter is to be

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Exponents are a "short cut" method of showing a number is multiplied by itself. Exponents can be shown to different ways. Example: x2 or x^2

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Know the difference between -x^y and (-x)^y. Example: -34 = -(3)(3)(3)(3) = -81 (-3)4 = (-3)(-3)(-3)(-3) = 81

Multiplying exponents Ex. X 2 * X 3 =X 5

Instead of actually multiplying the exponents, you add them. Remember that you can never multiply to exponents if their coefficient is different (X2 * E4=XE6 ) Which is the correct answer/answers for multiplying exponents? A) D2 * R7 = DR9 B) X 2 * X 3 =X 5 C) R1* R 9=R10 Answer: B and C A is not a correct answer because it is multiplying two exponents, that’s coefficients are not the same

Dividing exponents Ex.125/123=122 Instead of actually dividing the exponents also, you subtract them. If the coefficient of the exponent is the same on both sides of the division sign then just subtract the exponents. But if there are numbers that are different on both sides of the division sign (Ex. 125/43), then divide the different numbers and subtract their exponents. Instead of actually dividing the exponents also, you subtract them Which is the correct answer/answers for dividing exponents? A) E2 / E7 = E-5 B) 95/3 2 =3 3 C) Q9/ Q 3=Q3 Answer: A and B Problem C did not subtract the exponents, instead it divided them. REMEMBER: In order to divide exponents, you need to SUBTRACT the exponents and not divide them. Simplifying exponents Which of these problems simplifies the exponent correctly to the most simplest form? A) X3=X3 *X3 *X3 B)322 = 32*32 C) R9/ R 3=R3

Answer: B Problem A is wrong because it is not simplifying X3, but making it X9. And C is wrong because even though it did simplify once, it did not simplify to the simplest form.

Negative exponents A negative exponent means to divide by that number of factors instead of multiplying. So 4−3 is the same as 1/(43), and x-3 = 1/x3 Which of the following is the correct simplified answer for 46−3? A) Milker Jon

B) 46*46*46

C) 1/463

Answer:C Answer A is wrong because it is completely irrelevant to the problem. Answer B could have been right, but the person forgot to make it 1/46*46*46 which is the same as 1/463. Simplifying negative exponents Ex. 12−5=1/125=1/12*12*12*12*12=1/248,832 Put in the rule for negative exponents and then simplify Investment- An asset or item that is purchased with the hope that it will generate income or appreciate in the future Ex. I invest in a company for $500.

Rate- the amount of a charge or payment with reference to some basis of calculation: a high rate of interest on loans Simple interest Compound Interest- Interest computed on the accumulated unpaid interest as well as on the original principal Ex. If you invest a principal of $1000 at 10% compound interest paid monthly, then after the first month, the interest payment will be:interest (first month) = 10% of $1000 = $100

Compound interest formula

INTEREST FREQUENCIES Annual interest Once a year Bi-annual interest Every 2 years Semi-annual interest Twice a year Quarterly interest Four times a year Monthly interest 12 times a year Daily interest 365 times a year Factor- one of two or more numbers, algebraic expressions, that when multiplied together produce a given product; a divisor: 6 and 3 are factors of 18

Converting an equation to a table Identifying correct graph with correct equation Graphing exponential equations Exponential growth: when a quantity changes by a percentage