Lab3-SP12

# Well use the form f t pa t and determine the unknown

• Notes
• 10

This preview shows pages 3–6. Sign up to view the full content.

We’ll use the form f ( t ) = Pa t and determine the unknown constants P and a . To find P , evaluate f ( 0 ) in two ways. First We were told that f ( 0 ) = 3. Second Evaluate the general formula at t=0. f ( 0 ) = Pa 0 = P · 1 = P . Combining these we find that P = 3. Then, setting P = 3, we have: f ( t ) = 3 a t . To find the value of a , evaluate f ( 4 ) in two ways. First f ( 4 ) = 109. Second f ( 4 ) = 3 a 4 . Combining, we have 109 = 3 a 4 and we can solve for a : a 4 = 109 3 , and therefore a = 109 3 1 / 4 2.455140276. (This decimal value is the calculator’s best approximation to the correct value.) Now let’s see how rounding too soon affects calculations. . . 3

This preview has intentionally blurred sections. Sign up to view the full version.

Problem 2. In this problem you will calculate f ( 9.5 ) by first using a rounded-off value for a and then by using a more precise value of a . a. (i) Using the rounded-off value a = 2.5 , write the equation for f ( t ) . (ii) Use this equation (with the rounded value of a ) to find f ( 9.5 ) . Round the result to the nearest integer. b. (i) Compute ( 109 3 ) 1 / 4 and store that value in A . [See notes on next page.] Similarly store 3 into P . (ii) Compute f ( 9.5 ) = Pa 9.5 by typing: P × A x y x 9.5 Round the result to the nearest integer. c. Subtract your answer to part (ii) of (a) from your answer to part (ii) of (b). This number is the error introduced by rounding a . Notice that the value that you found in 2(c) is not zero! Lesson: Before calculating f ( 9.5 ) , you first found P and a . Errors in the calculations are magnified when larger exponents are involved. Small errors in a and P can lead to large errors in the final answer. It makes sense to avoid rounding values that you use in another calculation. From now on, If you calculate a value, don’t retype that value in your calculator later. Use the calculator memory! Round off only after the final value is computed! 4
3 Using Calculator Memories These instructions are designed for TI-83 and TI-84 calculators. If you have a different calcu- lator, look in the calculator’s instruction book. Suppose you finish a calculation. The “current value” is the quantity just computed, appearing on the bottom line of the calculator display. The symbol ANS appears near the bottom, right corner of the keyboard and is accessed by pressing the two keys 2nd and (-) , one after the other. We will write A NS instead of those two keystrokes. Type 3.45678 E NTER to get that number as the current value. To compute e 3.45678 we can type e x A NS ) E NTER . The displayed answer is 31.71469062. Typing the same keystrokes again won’t yield the same result, because A NS now stands for 31.71469062.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Spring '08
• Mcginnis

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern