Hand In Quizzes Powerpoint Templates Page 1 Exponential

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Hand In Quizzes Powerpoint Templates Page 1

Hand In Quizzes Powerpoint Templates Page 1

Exponential Functions Section 4. 2 Powerpoint Templates Page 2

Exponential Functions Section 4. 2 Powerpoint Templates Page 2

Basic Exponential Functions x f(x)=c We call it the exponential function in base c

Basic Exponential Functions x f(x)=c We call it the exponential function in base c Asymptote: x-axis (the function has no zero) c is called the periodic multiplicative factor Powerpoint Templates Page 3

Basic Exponential Functions x f(x)=c c cannot be: 1, 0 or negative The most

Basic Exponential Functions x f(x)=c c cannot be: 1, 0 or negative The most common bases are 10 and e Powerpoint Templates Page 4

Example 1 If the point A(2, 9) belongs to the graph of a basic

Example 1 If the point A(2, 9) belongs to the graph of a basic exponential function, determine the rule Step 1 – Plug it in 9 = c 2 Step 2 – Multiply exponent by reciprocal 9½ = c 2∙½ 3=c Step 3 – Write the Rule y = 3 x Powerpoint Templates Page 5

Exponential Functions b(x-h) f(x)=ac + a affects the vertical stretch a is also the

Exponential Functions b(x-h) f(x)=ac + a affects the vertical stretch a is also the initial value a can also flip the function (full examples on p. 142) Powerpoint Templates k a=3 a=1 Page 6

Exponential Functions b(x-h) f(x)=ac + b affects the horizontal stretch b=1/2 b is the

Exponential Functions b(x-h) f(x)=ac + b affects the horizontal stretch b=1/2 b is the period b cannot flip the function (full examples on p. 144) k b=1 b=2 b=1/4 b=1/10 Powerpoint Templates Page 7

Exponential Functions b(x-h) f(x)=ac + k h shifts the initial value to the right

Exponential Functions b(x-h) f(x)=ac + k h shifts the initial value to the right or left k shifts the initial value up or down k is the horizontal asymptote Do Activity 4 (don’t worry about transformations) Powerpoint Templates Page 8

Exponential Functions b(x-h) f(x)=ac + k FINDING THE ZEROS Plug in y=0 and solve

Exponential Functions b(x-h) f(x)=ac + k FINDING THE ZEROS Plug in y=0 and solve for x! y=5(3)x-2 – 15 0=5(3)x-2 – 15 15=5(3)x-2 15/5=(3)(x-2) 3=(3)(x-2) 1 = x-2 3=x Powerpoint Templates Page 9

Word Problem Example A mosquito population doubles every seven days. If there were 5

Word Problem Example A mosquito population doubles every seven days. If there were 5 mosquitoes initially, after how many days will the population grow to 80? a = initial value = 5 c = base = 2 b = period = 1/7 (once every seven days) No h and k Powerpoint Templates Page 10

Word Problem Example A mosquito population doubles every seven days. If there were 5

Word Problem Example A mosquito population doubles every seven days. If there were 5 mosquitoes initially, after how many days will the population grow to 80? Rule: y = 5(2)t/7 80 = 5(2)t/7 16 = (2)t/7 24 = (2)t/7 4 = t/7 28 = t Powerpoint Templates Page 11

HOMEWORK • • • Page 140 2, 3, 4, Page 142 #2 Page 143

HOMEWORK • • • Page 140 2, 3, 4, Page 142 #2 Page 143 #3, 4, 5 Page 145 #8 (the rule: y=24 t Page 148 #13 (pull out the b) Page 150 #15, 16, 17, 19 a (4 because 15 minutes happens 4 times in an hour!)) Powerpoint Templates Page 12