Explain the lesson and explain your answers must have concrete evidence

Exponential Function Definition: An exponential function can be written as f(x) = b, where b > 0, b # 1, and x is any real number In the equation f(x) = b*, b is a constant called base and x is an independent variable called exponent Examples: f (x) = 3x g(x) = 10x h(x) = 2x+1 51nenti -- - ' . . . r\"! \"mum 1'0 81 function is the set of real numbers and the range is the set at all mistrust ' Cwyou cite tom 33 - 1* is": \"1"" we can apply exponential function in our life? ' opulatlon growth 2. Growth and decay . 3. Increase of prices of commodities 4.' The value of brand-new cars ' Examples 1. The number of pupils at Exponent Primary School has increased by 40 each ot'thc past ve years. If the Population was 500 five years ago, what is the present population? SOLUTION: The number of pupils increased by the same amount each year, so this represents a linear function. ' Because the pupils\" population increased by 40 per year. in ve years it will grew by 5 x 40 =200 pupils, from 500 it will become 700. \"'1' represents the number of pupils in t years, the function would be P = 500+40t 2. The initial population at Brgy 127 is 10,000 people. Brgy 127 grows at a constant rate of 10% per year. What would be the population of this bamngay aer 4 years? SOLUTION: If P represents the total population and t represents time, then =initia1 pOpulation times (rate)', thus P = 10000 +(1.10)4 = 1464] population of Brgy. 127 aer 4 years. 1.10 the growth factor 100% +10% = 110% =1.10 3. Determine the growth factor of the quantity that increases by the given percent. a. 50% 100% +50% = 150% = 1.50 b. 75% 100% +75% = 175% = 1.75 c. 10% 100%+10%=110%=l.10 d. 12.5% 100% + 12.5% = 112.5% = 1.125 e. 4. Emerson deposits P50000 in a savings account. The account pays 6% annual interest. If he makes no more deposits and no withdrawals, calculate his new balance after 10 years. Solution: 6% the interest rate per year Growth factor would be: 100% +6% = 10 % = 1.06 Equation would be y = P50000 (1.06)\"), where y represents the new ba1ance y = P8954238 New balance aer 10 years The rule for exponential growth can be modeled by y=ab', where a is the starting number, b is the growth factor, and x is the number of intervals 5. A bacteria grows at a rate of 25% each day. There are 500 bacteria today. How many bacteria will be 3. Tomorrow? . SOLUTION: y=abx , a=500 b= 1.25, x=1 y = 5000.25)" ' y = 625 bacteria therefore, there will be 625 bacteria tomorrow 13. One week from now? SOLUTION: y= abX a= 500 1 xe c. (3)32:+5 _<_ e x s x_6 rewrite as and negative law of exponents distributive property put similar terms on the same side simplify to both sides reverse inequality symbol revised knowledge: actual answer process questions focus questions. why are exponential equations inequalities important functions can be used model growth decay. everincreasing so saying that an function models population exactly means human will grow without bound. how rnctions help solve real-life problems represent real-world applications such bacterial compound interest. final generalization synthesis summary gimme-w have many in real life. they involve decay interest investment or a loan appreciation depreciation market value particular product. even utilized i phenomenon at some constant conditions. l tctivity a. tell whether each following statements is true false. write your before number. l. dened by f any equal rst differences its values. value. y="3x4" equation function. number solution has no solution. b. inequalities. p: c. word problems: what asked. certain town la union year increases rate about factor b determine p t years. c using if continues increase people there d aaron invested amount annual find he total money after years>