Presentation on theme: "Jules Henri Poincaré ( ) France"— Presentation transcript:
1Jules Henri Poincaré (1854-1912) France Jules Henri Poincaré ( ) France. Known as a mathematician, theoretical physicist, philosopher of science and engineer. He left an impact on pure and applied mathematics along with mathematical physics, and celestial mechanics.Poincaré quote: “The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.”
2Warm Up 1. Write 0.03 as a percent. 2. Write as a decimal. Find each value. Round to the nearest tenthif necessary.3. Find 10% of 53.3%0.0455.3
3Objectives Use common applications of percents. Estimate with percents.
4Caution!You must convert a percent to a decimal or a fraction before doing any calculations with it.
5Example 1: Business Application Mr. Cortez earns a base salary of $26,000 plus a sales commission of 5%. His total sales for one year were $300,000. Find his total pay for the year.total pay = base salary + commissionWrite the formula for total pay.= base + % of total salesWrite the formula for commission.= 26, % of 300,000Substitute values given in the problem.= 26,000 + (0.05)(300,000)Write the percent as a decimal.= 26, ,000Multiply.= 41,000Add.Mr. Cortez’s total pay was $41,000.
6Check It Out! Example 1A telemarketer earns $350 per week plus 12% commission on sales. Find her total pay for a week in which her sales were $940.total pay = base salary + commissionWrite the formula for total pay.= base + % of total salesWrite the formula for commission.= % of 940Substitute values given in the problem.= (0.12)(940)Write the percent as a decimal.=Multiply.=Add.The telemarketer’s total pay was $
7I = P r t Simple Interest Paid Annually Interest is the amount of money charged for borrowing money, or the amount of money earned when saving or investing money. Principal is the amount borrowed or invested. Simple interest is interest paid only on the principal.Simple Interest Paid AnnuallyI=PrtSimple interestTime in yearsPrincipalInterest rate peryear as a decimal
8Example 2A: Financial Application Find the simple interest paid for 3 years on a $2500 loan at 11.5% per year.I = PrtWrite the formula for simple interest.I = (2500)(0.115)(3)Substitute known values. Write the interest rate as a decimal.I =Multiply.The amount of interest is $
9Example 2B: Financial Application After 6 months, the simple interest earned on an investment of $5000 was $45. Find the interest rate.Write the formula for simple interest.I = PrtSubstitute the given values.Multiply Since r is multiplied by 2500, divide both sides by 2500 to undo the multiplication.45 = 2500r0.018 = rThe interest rate is 1.8%.
10Helpful HintWhen you are using the formula I= Prt to find simple interest paid annually, t represents time in years. One month is year.
11Check It Out! Example 2aFind the simple interest earned after 2 years on an investment of $3000 at 4.5% interest earned annually.Write the formula for simple interest.I = PrtI = (3000)(0.045)(2)Substitute the given values.Multiply.I = 270The interest earned is $270.
12Check It Out! Example 2bThe simple interest paid on a loan after 6 months was $306. The annual interest rate was 8%. Find the principal.Write the formula for simple interest.I = Prt306 = (P)(0.08)Substitute the given values.Multiply Since P is multiplied by 0.04 , divide both sides by 0.04.306 =.04P7650 = PThe remaining principal is $7650.
13Practice1. A computer salesperson earns a base salary of $32,000 per year plus a commission of 6% on total sales. Total sales for one year were $350,000. Find the salesperson’s total pay for the year.$53,0002. Find the simple interest paid for 9 months on a a $500 loan at 8% per year.$303. After 2 years the simple interest earned on an investment of 4000 was $216. Find the interest rate.2.7%
14Practice4. A family’s dinner check was $ Estimate a 15% tip.About $6.005.The sales tax rate is 7.1%. Estimate the sales tax on a television set that costs $399.About $28