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19

Ti36eng1.doc   TI-36X II Manual   Linda Bower   Revised:
01/10/03 10:47 AM   Printed: 01/10/03 10:47 AM   Page 19 of
48

³

Problem

A radioactive substance decays exponentially. If y

o

grams of certain radioactive substance are initially
present, the number of grams y(t) after t days is given
by the formula:

y(t)=y

o

e

-0.00015t

After 340 days, how much of a 5-gram sample of this
radioactive substance remains? After 475 days? Store
the constant part of the exponent to memory so you
need enter it only once. Round results to two decimal
places.

J

0

I

0 0 0 1 5

S V

L

0.00015

Þ

A

ß

L

0.00015

DEG

5

< % d " " " V

R <

3 4 0

O V

5

è

e^(A

è

340) 

ß

4.751393353

DEG

% t

2

5

è

 e^(A

è

340) 

ß

4.75

FIX

DEG

5

< % d " " " V

R <

4 7 5

O V

5

è

e^(A

è

475) 

ß

4.66

FIX

DEG

About 4.75 grams of this radioactive substance remain
after 340 days, and 4.66 grams remain after 475 days.

Summary of Contents for TI-36X II

Page 1: ...c TI 36X II Manual Linda Bower Revised 01 10 03 10 47 AM Printed 01 10 03 10 47 AM Page 0 of 48 TI 36X Scientific Calculator USER S GUIDE 2000 2003 Texas Instruments Incorporated education ti com ti c...

Page 2: ...ns 6 Basic Operations 7 Last Answer 7 Percent 9 Fractions 10 Exponents Roots and Reciprocals 11 Notation 12 Pi 13 Memory 14 Stored Operations 16 Logarithms 18 Trigonometric Functions 20 Angle Modes 22...

Page 3: ...nutes Press T after APD to power up again the display pending operations settings and memory are retained Alternate Functions Most keys can perform two functions The first function is marked on the ke...

Page 4: ...a negative sign a x10 indicator and a 2 digit positive or negative exponent Results that exceed the digit limit are displayed in scientific notation Note In the text numbers containing decimal fractio...

Page 5: ...to the current entry However if the argument is another function you need to press V to select the first function before proceeding to the next To return to the previous screen without selecting the m...

Page 6: ...r is on a character deletes the character under the cursor If the cursor is at the end of an entry deletes the character to the left of the cursor Lets you insert one or more characters at the cursor...

Page 7: ...ientific or engineering notation is active STAT Calculator is in Statistics mode DEG RAD or GRAD Specifies angle unit setting degrees radians or grads The default is the degree setting HEX or OCT Calc...

Page 8: ...gic NOT and 2 s complement 3rd Fractions 4th Functions that are entered after the argument such as x 2 and angle unit modifiers r g metric conversions 5th Exponentiation and roots x 6th Negation L 7th...

Page 9: ...0 through 9 Adds subtracts multiplies divides N O Opens closes a parenthetical expression I Inserts the decimal point J Enters a negative sign V Completes all operations Last Answer u recalls the valu...

Page 10: ...0 03 10 47 AM Page 8 of 48 Examples 5 9 6 2 V 5 9 6 2 49 DEG 5 N 9 6 O 2 V 5 9 6 2 73 DEG W 8 8 7 Ans 8 7 8 390804598 DEG t F0123456789 DEG V Ans 8 7 8 391 FIX DEG 5 2 u t 6 V 5 2 Ans 18 390805 FIX DE...

Page 11: ...concentration and 8400 tons having a 3 1 percent concentration How much metal does the company get in total from the three quantities of ore If the metal is worth 280 per ton what is the value of the...

Page 12: ...st be positive integers To negate a fraction or a mixed number press J before entering the first argument Converts from mixed number to simple fraction and vice versa _ Converts from fraction to decim...

Page 13: ...the number is negative the power must be an integer If you include an operation in the exponent you must use parentheses n Calculates the square root of a positive value j Calculates any root of any...

Page 14: ...ientific notation The format of scientific notation is n x 10 p where 1 n 10 and p is an integer ENG Engineering notation exponent is a multiple of 3 These modes affect only the display of results and...

Page 15: ...it Examples Find the circumference and the area of a circle having a radius of 5 centimeters Find the surface area of a sphere having a radius of 5 centimeters Remember circumference 2pr area pr 2 sur...

Page 16: ...variable Press V and the value of your last answer is stored into the variable you have selected If that variable already contains a value the new one will replace it If you enter an expression and pr...

Page 17: ...0 meters What volume of gravel would the company remove from each if they excavated to a depth of 150 meters To a depth of 210 meters Display results in engineering notation Z V 3 5 0 5 6 0 S V 350 56...

Page 18: ...aracters or items 3 Press V to save the operation to memory 4 Each subsequent time you press 2 or 3 the TI 36X recalls the stored operation and applies it to the last answer The expression with the st...

Page 19: ...wer Revised 01 10 03 10 47 AM Printed 01 10 03 10 47 AM Page 17 of 48 Examples b 2 V OP1 2 DEG 3 2 3 2 1 6 DEG 2 6 2 2 12 DEG 2 12 2 3 24 DEG c 5 V OP2 5 DEG 1 0 3 10 5 1 15 DEG 3 15 5 2 20 DEG 3 20 5...

Page 20: ...number 10 Raises 10 to the power you specify ln Yields the logarithm of a number to the base e e 2 718281828495 e Raises e to the power you specify Select the function on the menu then enter the valu...

Page 21: ...y t yoe 0 00015t After 340 days how much of a 5 gram sample of this radioactive substance remains After 475 days Store the constant part of the exponent to memory so you need enter it only once Round...

Page 22: ...ect the desired function enter the value and close the parentheses with O Set the desired angle mode before starting trigonometric calculations The problems below assume the default which is degree mo...

Page 23: ...b Measurements of length and height are in meters Round off results to one decimal place Remember 3 7 tan a so a tanL1 3 7 Then 3 h sin a so h 3 sin a Then 7 h sin b so b sinL1 7 h t 1 e 3 7 O V tan 1...

Page 24: ...ts you convert an angle to DMS Notation 4DMS You can use a DMS value in calculations but then the results will no longer be in DMS format the calculator will automatically convert to decimal format Pr...

Page 25: ...probably know that 30 6 radians In the default Degree Mode find the sine of 30 Then set the calculator to Radian Mode and find the sine of 6 radians e 3 0 O V sin 30 0 5 DEG V 5 6 O V sin 6 0 5 RAD Yo...

Page 26: ...rting separated by a comma then close the parentheses with O before you complete the operation with V Set angle mode as necessary before starting calculations Examples Convert polar coordinates r 5 30...

Page 27: ...1 Angle modes do not affect hyperbolic calculations Problem Given the hyperbolic function y 3cosh x 1 Find the value of y when x 2 and x 5 Round off results to one decimal place Use the Stored Operati...

Page 28: ...meters to feet feet to meters mP0 3048 ftQ0 3048 m yd meters to yards yards to meters mP0 9144 ydQ0 9144 km mile kilometers to miles miles to kilometers kmP1 609344 mileQ1 609344 l gal US liters to U...

Page 29: ...decimal places 1 0 km mile DEG V V t 2 10 km mile 6 21 FIX DEG 5 0 V V 50 mile km 80 47 FIX DEG Problem Under a pressure of one atmosphere ethyl alcohol freezes at L117 C and boils at 78 5 C Convert t...

Page 30: ...s 9 10938188Q 10 31 kilograms mp proton mass 1 67262158Q 10 27 kilograms mn neutron mass 1 67492716Q 10 27 kilograms mm muon mass 1 88353109Q 10 28 kilograms G universal gravitation 6 673 Q 10 11 Newt...

Page 31: ...rest whole number The formula for distance fallen is y L 1 2 gt 2 where t time in seconds and g gravitational acceleration 9 80665 meters per second squared We measure the y coordinate from the positi...

Page 32: ...Error will display and A B and C will be cleared If you want to solve a given problem again using a different number of intervals or different limits enter values to store in memory variables A B and...

Page 33: ...48 Problem Find 0 2 sin a cos a da using 10 intervals Solve the problem again using 20 intervals V 0 S V 0 A 0 RAD 5 2 S V 2 B 1 570796327 RAD 1 0 S V 10 C 10 RAD 0 e V R O e V R O V CALC RAD sin A c...

Page 34: ...f objects is not important as in a hand of cards The factorial of n is the product of the positive integers from 1 to n n must be a positive whole number 69 RAND Generates a random real number between...

Page 35: ...2 5 52 2598960 DEG You no doubt recognize the above formula to find the number of possible combinations of n objects taken r at a time without replacement You can obtain this result more directly by u...

Page 36: ...y a b ln x EXP Analyzes paired data with 2 measured variables Yields regression equation in the form y ab x PWR Analyzes paired data with 2 measured variables Yields regression equation in the form y...

Page 37: ...ered You can change or delete data points by scrolling to the desired point and editing or pressing If you are in 2 VAR mode you must delete both the data point and the frequency You can add new point...

Page 38: ...when N no is underlined to return to the previous screen without exiting STAT mode Variables Definition n Number of X or X Y data points or Mean of all X or Y values Sx or Sy Sample standard deviation...

Page 39: ...48 China 424 3 35 Using the LIN regression find the equation representing the best fit in the form y a bx where x GDP capita and y telephone density Find the coefficient of correlation Use this equat...

Page 40: ...STAT DEG x y FIX STAT DEG 1 0 6 9 5 O V t 2 y 10695 24 08 FIX STAT DEG 8 5 I 6 8 O V t 0 x 5 68 1126 FIX STAT DEG The equation is y 3 5143 0 0019x The coefficient of correlation is 9374 A country with...

Page 41: ...OR 0 OR 0 0 0 OR 1 1 1 OR 1 1 XOR 0 XOR 0 0 0 XOR 1 1 1 XOR 1 0 NOT NOT 0 1 NOT 1 0 2 s 2 s complement Except for NOT and 2 s complement these functions compare the corresponding bits of two values T...

Page 42: ...uld keep the calculator in the decimal mode because some of the calculator s operating features are limited or nonexistent in the other modes Selects octal mode You can enter positive octal numbers as...

Page 43: ...rst Operations with complex numbers are limited to J and the functions in the menu below When you perform computations with complex numbers the result line displays the real part of the answer and r s...

Page 44: ...imag Returns the imaginary part of a complex number abs Returns the absolute value of a number Problem Find the product of 4 2i and 3 5i display the imaginary part as well as the real part of the res...

Page 45: ...attempted to divide by 0 In statistics n 1 SYNTAX The command contains a syntax error entering more than 23 pending operations 8 pending values or having misplaced functions arguments parentheses or...

Page 46: ...y in Hex out of range 2 39 For log or ln x 0 For tan x 90 90 270 270 450 etc For sin 1 or cos 1 x 1 For tanh 1 x x 1 For cosh 1 0 For cosh 1 x x 0 For nCr or nPr either n or r is not an integer 0 1E1...

Page 47: ...ts Battery Replacement Replace protective cover Place the TI 36X face down 1 Remove screw case using a small Phillips screwdriver 2 Carefully separate front from back starting from the bottom Caution...

Page 48: ...ducts and services contact TI by e mail or visit the TI calculator home page on the world wide web e mail address ti cares ti com Internet address education ti com Service and Warranty Information For...

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