Transcript SolveExEqus
Solving Exponential Equations Remember, when you are solving an equation, you are trying to the find the value of the unknown that makes the left side equal the right side There are 3 methods used to solve an equation: 1. Inspection 2. Guess and Check 3. Operations Solve the following: x + 7 = 10 by inspection x=3 4–3=x x=1 by inspection Solve the following: x + 17 = 35 by guess x = 18 42 = x x = 16 and check Solve the following: x2 = 9 x = 3 or -3 The last kind of example represents the lesson today. The variable could be the exponent… Solve the following 2x = 32 x=5 NOTICE, we can re-write 32 as a power of 2 (if you can not inspect) 2x = 25 Since the bases are equal, the exponents must be as well. We will use this re-writing technique when we can not solve by inspection 4x + 1 = 2x - 1 4x + 1 = 2x - 1 (22)x + 1 = 2x - 1 22x + 2 = 2x - 1 2x + 2 = x - 1 Since 4 = 22 • P of P • Dis Prop Since the bases are equal, so are the exponents, therefore we can create a new equation using just the exponents. 2x + 2 = x - 1 -x -x 1x + 2 = - 1 -2 -2 x = -3 Does x = -3 work? 4x+ 1 = 2x - 1 4-3 + 1 = 2-3 – 1 ? 4-2 = 2-4 1 = 1 42 24 1 = 1 16 16 YES! 93x + 1 = 27x (32)3x + 1 = (33)x 36x + 2 = 33x 6x + 2 = 3x -3x -3x 3x + 2 = 0 Since 9 = 32, and 27 = 33 • P of P • Dis Prop Since the bases are equal, so are the exponents, therefore we can create a new equation using just the exponents. Exponential Decay Iodine – 131 is used to determine if a person has a thyroid deficiency. • The thyroid (from the Greek word for "shield", after its shape) is one of the larger endocrine glands in the body. It is a double-lobed structure located in the neck and produces hormones, principally thyroxine (T4) and triiodothyronine (T3), that regulate the rate of metabolism and affect the growth and rate of function of many other systems in the body. The hormone calcitonin is also produced and controls calcium blood levels. Iodine is necessary for the production of both hormones. Hyperthyroidism (overactive thyroid) and hypothyroidism (underactive thyroid) are the most common problems of the thyroid gland. Specialists are called Thyroidologists. Iodine – 131 is injected into the patient. A healthy thyroid will absorb all the iodine. An exponential equation will tell them how much iodine to look for. t AL = AO 1 2 8.2 AL = the amount of iodine left AO = the original amount of iodine t = the elapsed time in days How long should it take 80mg of iodine to decay into 5 mg? Homework Page 23 [1-9] odd