Test 1 Review Test 1: 15 questions total 13 multiple choice worth 6 points each 2 free response questions (worth 10 or 12 points) Scientific Notation: Scientific Notation is a shorter way of writing very large or very small numbers. Look at these two numbers: 2,350,000,000,000,000,000 0.00000000000015 When we use scientific notation, we write these two numbers as: 2.35 X 10 18 and 1.5 X 10 13 To write a number using scientific notation, write it as a product so that The first factor is greater than 1 and less than 10. The second factor is a power of 10. To write a number using scientific notation, imagine that there is a decimal after the first non-zero digit. Then count the number of decimal places to the actual decimal point. This will give you the power of 10 that you should write in your answer. If the power of 10 is positive, move the decimal point to the right. If the power of 10 is negative, move the decimal point to the left. Examples: Write using scientific notation. 1. 125,000
2. 36,000,000 3. 0.000028 4. 0.00000000002 Write as a decimal number. 5. 3.1 X 10 5 6. 4.826 X 10 12 7. 1.38 X 10 3 8. 9.167 X 10 8 Decimal Places 5, 8 9 2, 6 4 3
5, 8 9 2, 6 4 3. 7 1 8 2 3 9 How do they get their names? 6 7 9. 3 2 8 1 5 Example: a) Round 76.246 to the nearest tenth. b) Round 34.694 to the nearest tenth.
Exponents a b Basic Rules of Exponents ( for a > 0) Zero Exponent : a 0 = 1 Product Law : a b a c = a b+c Quotient Law : ab ac = ab c Power Law: (a b ) c = a bc Negative Exponents : a b = 1 a b Fractional Exponents: a 1 b b = a Examples: a) 2 3 X 2 2 = b) x 5 = c) x 2 = d) x 2 y 2 = e) 100 1 2 =
f) x 2 y 0 = g) 2 3 = h) x 1 = i) 16 1 2 = j) 2 1 + 5 1 = k) x 2 + y 0 = Order of Operations 1. Parentheses 2. Exponents 3. Multiplication / Division 4. Addition / Subtraction ( PEMDAS) Examples: a) 4 + 3 7 = b) (3 + 5) 2
c) 12X6 3 = d) 3 X 2 2 = e) (2x) 2 = f) ( 2x) 2 = g) 3(2 + 3x) = h) (3 2) 2 = i) 12 6 X 2 = j) (3 X 2) 2 = k) 3(2x) 2 = l) (2x) 2 = m) 3(1 + 2 x) =
n).6 7 = o) 2 1 +3 1 = p) 9 6 62 7+3 9 = Average Rate of Change AROC = f(x 2 ) f(x 1) x 2 x 1 Example: A breeding group of foxes is introduced into a protected area and exhibits logistic population growth. After x years, the number of foxes is given by F(x) = 25.5 0.23 + 0.76 x What is the average rate of change in the fox population between the 6 th and 9 th years in this area? Round to two decimal places.
Using Rate of Change to Estimate The following table gives values for a function N = N(t). Calculate the average rate of change from t = 10 to t = 20. Use your answers to estimate the value of N(11). Concavity Facts A function is decreasing but : (a) at an increasing rate (b) at a decreasing rate A function is increasing but : (a) at an increasing rate (b) at a decreasing rate
Word Problems Charles needs a cable that is 11 inches long. If the cable costs $ 1.80 per centimeter, approximately how much would he pay for the entire cable? Show how to set up the calculation to solve this problem. Note that 1 inch = 2.54 c.m. Suppose you want to buy a pair of shoes that cost $ x. The shoes are currently on sale for 30% off. When you purchase the shoes, you will have to pay 9% sales tax. Show how to set up the calculation to determine the total you must pay for the shoes.
City water, which is slightly chlorinated, is being used to flush a tank of heavily chlorinated water. The concentration C = C(t) of chlorine in the tank t hours after flushing begins is given by C(t) = 0.1 + 2.76e 0.32t milligrams per gallon. What is the initial concentration of the chlorine tank. Function P(M, r, t) = M X 1 1 X (1 r (1+r) t) shows the amount of money P, in dollars, that you can afford to borrow at a monthly interest rate of r (as a decimal) if you are able to make t monthly payments of M dollars. How much money can you afford to borrow at the monthly interest rate of 0.9% if you can afford to pay $300 per month for 3 years.
Suppose that you are getting married and planning your wedding. It costs $3600 to rent the banquet hall and it includes a catered lunch for 50 guests. For each additional guest the catered lunch costs $35. Find a formula showing the cost of the wedding venue and lunch if n guests are invited. Assume that n is at least 50.
A boat rental company charges a daily rental fee of $40 with an additional fee of $7 for each person in the boat. Suppose that n boats are rented on a given day be a total of p people. Let R represent the revenue that the company makes on a given day. Write an equation for R terms of n and p. This past Saturday, the boat rental company rented 16 boats to be used by 44 people. Use your revenue function to determine the boat company s revenue on Saturday.