Exponential and Logarithm functions KUS objectives BAT Solve
Exponential and Logarithm functions • KUS objectives BAT Solve real life problems involving growth functions of the form y = Aebx+c
Real life problems: growth functions Think Pair Share a) Calculate the value of the car when it is new The new price implies t, the time, is 0… Substitute t = 0 into the formula… -t 10 P = 16000 e - P = 16000 e 0 P = 16000 e P = £ 16000 0 10
WB 15 solution • -t 10 P = 16000 e - P = 16000 e 5 10 -0. 5 P = 16000 e P = £ 9704. 49 3 A
WB 15 solution -t 10 • P = 16000 e P = 16000 x 0 P = £ 0 -t 10 e 1 (10√e)t Bigger t = Bigger denominator = Smaller Fraction value… 3 A
WB 15 solution P • £ 16000 -t 10 P = 16000 e t t is independent so goes on the x axis P is dependant on t so goes on the y axis 3 A
WB 16 The number of elephants in a herd can be represented by the equation: Where n is the number of elephants and t is the time in years after 2003. a) b) c) d) Calculate the number of elephants in the herd in 2003 Calculate the number of elephants in the herd in 2007 Calculate the year when the population will first exceed 100 elephants What is the implied maximum number in the herd? a) Calculate the number of elephants in the herd in 2003 Implies t = 0 t=0 e 0 = 1 Think Pair Share
WB 16 solution b) Calculate the number of elephants in the herd in 2007 Implies t = 4 t=4 Round to the nearest whole number c) Calculate the year when the population will first exceed 100 elephants Implies N = 100 Subtract 150 Divide by -80 Take natural logs 2003 + 19 = 2022 Multiply by 40
WB 16 solution d) What is the implied maximum number in the herd? Implies t ∞ Rearrange As t increases Denomintor becomes bigger Fraction becomes smaller, towards 0
WB 17
KUS objectives BAT Solve real life problems involving growth functions of the form y = Aebx+c self-assess One thing learned is – One thing to improve is –
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