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8.1 Exploring Exponential ModelsPowerPoint Presentation

8.1 Exploring Exponential Models

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## PowerPoint Slideshow about ' 8.1 Exploring Exponential Models' - jeremy-castro

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Given the general form y=abx

When b > 1, b is the growth factor

Growth Factor, Decay Factor- When 0 < b < 1, b is the decay factor

What is an asymptote?

“Walking halfway to the wall”

An Asymptote is a line that a graph approaches as x or y increases in absolute value.

In this example, the asymptote is the x axis.

Graphing Exponential Functions

Complete the table using the integers -3 through 3 for x.

Let’s try one

Complete the table using the integers -3 through 3 for x. Then graph the function.

Let’s try one

Complete the table using the integers -3 through 3 for x. Then graph the function.

Writing Exponential Equations

- Find the exponential equation passing through the points (3,20) and (1,5).

Start with the general form.

Choose a point. Substitute for x and y using (3, 20)

Solve for a

Substitute x and y using (1, 5) and a using

Division property of exponents

Writing Exponential Equations

- Find the exponential equation passing through the points (3,20) and (1,5).

Simplify

Solve for b

Go back to the equation for a; substitute in b and solve for a

Writing Exponential Equations

- Find the exponential equation passing through the points (3,20) and (1,5).

Going back to the general form, substitute in a and b

The exponential equation passing through the points (3,20) and (1,5) is

Let’s Try One

- Find the exponential equation passing through the points (2,4) and (3,16).

Start with the general form.

Choose a point. Substitute for x and y using (2, 4)

Solve for a

Substitute x and y using (3, 16) and a using

Division property of exponents

Writing Exponential Equations

Simplify

Solve for b

Go back to the equation for a; substitute in b and solve for a

Going back to the general form, substitute in a and b

The exponential equation passing through the points (2,4) and (3,16) is

Putting it all together . . .

- Find the equation of the exponential function that goes through (1,6) and (0,2). Graph the function.

Modeling Growth with an Exponential Equation

- The growth factor can be found in word problems using b = 1 + r
where r = rate or amount of increase. You can substitute your new b into your general equation to find the exponential function.

- EX- a guy puts $1000 into a simple 3% interest account. What is the exponential equation?

r = rate 3% (write as 0.03)

b = 1 + r = 1.03

x = time

a = amount put into the account ($1,000)

- EX – a colony of 1000 bacteria cells doubles every hour. What is the exponential equation?

r = 1 (why not 2?)

b = r + 1 = 2

x = time (in hours)

a = the original number in the colony (1,000 bacteria )

b = r + 1, where r is the amount of increase. We are increasing by 100% each time something doubles, so r = 1

- EX- a $15000 car depreciates at 10% a year. What is the exponential equation?

r = - 10% (the car is worth 10% less each year)

b = 1 - r = 1 – 0.1 = 0.9

x = time (in years)

a = amount put into the account ($15,000)

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