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The new amount of bacteria is all of the initial amount, 100%, plus 8% of the initial amount or 108% of the initial amount. The number of bacteria present one day later is equal to the initial amount plus how many grew in one day or the increase. First find how many bacteria will be present one day later? Find an equation that relates number of bacteria and days.Ī. The culture grows at a rate of 8% each day. There are 5,000 bacteria initially present in a culture. You need to invest $11,119.35 now in order to have $15,000 in ten years.Įxample 4.
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Substituted the values into the formula, F = P(1 + i) n. How much money should you invest at an annual interest rate of 3% if you want $15,000 in 10 years? Substituted the values into the variables.ī. Substitute the values into the formula, F = P(1 + i) n. You need to multiply 20 by 12 because there are 12 months in a year. Make a table of the information and variables in the problem.Įxplanation: You need to divide 0.06 by 12 because annual interest is per year and the formula is per month. If you invest $3,500 at an annual interest rate of 6%, how much money will you have after 20 years? When the interest is compounded monthly, the formula below computes how much money will be in your account at sometime in the future. Examples of accounts that use compound interest are savings accounts, certificates of deposit, savings bonds, and money market accounts.Įxample 3. Review the card as homework.įor many transactions, interest is added to the principal, the amount invested, at regular time intervals, so that the interest itself earns interest.
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Make a note card showing examples with and without parentheses and with even and odd exponents. Study Tip: Parentheses often make a difference in the answer. Generally, a negative number raised to an odd power will be negative. Generally any number raised to an even power will be positive.Įxplanation: Why are both answers negative?Ī negative times a negative three times is negative. Recall the order of operations: compute exponents before multiplication.Ī negative times a negative four times is positive. The explanation below is for the Tl-30x II S.Įxplanation: Why is -6.2 4 negative while (-6.2) 4 is positive? For other calculators, the exponent key is y x. The exponent key for the Tl-30x II S, the recommended calculator for the course, is ^. Use a calculator to compute the following. Three is the base and five is the exponent.Įxample 2. Write 3 5 using the definition of exponents. Vocabulary : b n means b times itself n times b is called the base and n is called the exponent.Įxample 1. In addition, you will solve problems using the formula for compound interest and tables for demonstrating bacteria growth to illustrate the applications of exponents. In this section, you will define exponents and perform computations with a calculator. A few more examples are shown in the table below.Chapter 3 - EXPONENTS AND ALGEBRAIC FRACTIONS INTRODUCTION TO POSITIVE EXPONENTS Objectives In this case, the “cents” means “hundredths of a dollar,” so this is the same as saying fifteen thousand, two hundred sixty-four and twenty-five hundredths. You would read this as fifteen thousand, two hundred sixty-four dollars and twenty-five cents. You can see this demonstrated in the diagram below, in which the last digit is in the ten thousandths place.Īnother way to think about this is with money. To read mixed numbers, say the whole number part, the word “and” (representing the decimal point), and the number to the right of the decimal point, followed by the name and the place value of the last digit. In the case of a decimal, a mixed number is also a combination of a whole number and a fraction, where the fraction is written as a decimal fraction. Recall that a mixed number is a combination of a whole number and a fraction. Note that the number is read as a fraction.Īlso note that the denominator has 2 zeros, the same as the number of decimal places in the original number.Īnswer The number 0.68 in word form is sixty-eight hundredths. The relationship between decimal places and fractions is captured in the table below. And to get to the hundreds place, you break the tenth into ten more pieces, which results in the fraction. You divide 1 by 10 ( ) to get to the tenths place, which is basically breaking one into 10 pieces. Notice that you continue to divide by 10 when moving to decimals. Now, suppose the balloon continues to lose volume, going from 1 liter, to 0.1 liters, to 0.01 liters, and then to 0.001 liters. Then, you divide 10 by 10 to get to the ones place, because there are 10 ones in 10. This is because there are 10 tens in 100. You divide 100 by 10 to get to the tens place. Notice that you’re dividing a place value by ten as you go to the right. Imagine that as a large balloon deflates, the volume of air inside it goes from 1,000 liters, to 100 liters, to 10 liters, to 1 liter.