Chapter 12  Objective 5.1  Exercises

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Use the compound interest formula  P =  A(1 +  i) n, where  A is the original value of an investment,  i is the interest rate per compounding period,  n is the total number of compounding periods, and  P is the value of the investment after  n periods.

1.  An investor deposits $8000 into an account that earns 12% interest compounded semi-annually. What is the value of the investment after 4 years?

2.  An investor deposits $5000 into an account that earns 12% annual interest compounded semi-annually. In approximately how many years will the investment be worth twice the original amount?

The percent of correct welds a student welder can make will increase with practice and can be approximated by the equation  P = 100[1 - (0.75) t], where  P is the percent of correct welds and  t is the number of weeks of practice.

3.  Find the percent of correct welds a student will make after four weeks of practice.

4.  How many weeks of practice are necessary before a student will make 95% of the welds correctly?

The percent of light that will pass through a material is given by the equation log  P = - kd, where  P is the percent of light passing through the material,  k is a constant that depends on the material, and  d is the thickness of the material in centimeters.

5.  The constant  k for a piece of tinted glass is 0.5. How thick a piece of this glass is needed so that 60% of the light that is incident to the glass will pass through it?

6.  The constant  k for a piece of opaque glass that is 0.5 cm thick is 0.4. Find the percent of light that will pass through the glass.

Use the Richter equation , where  M is the magnitude of an earthquake,  I is the intensity of its shock waves, and  I0 is a constant.

7.  How many times stronger is an earthquake that has magnitude 5.8 on the Richter scale than one that has magnitude 3.2 on the scale?

8.  How many times stronger is an earthquake that has magnitude 6.4 on the Richter scale than one that has magnitude 1.6 on the scale?

Use the pH equation pH = -log(H+), where H+ is the hydrogen ion concentration of a solution.

9.  Find the pH of a hydrogen chloride solution for which the hydrogen ion concentration is 5.2 x 10-5.

10.  Find the pH of a sodium hydroxide solution for which the hydrogen ion concentration is 4.6 x 10-7.

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