4.2 – Graph Exponential Decay Functions

GPS: MM3A2e, MM3A2f, MM3A2g

MM3A2e – Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change

MM3A2f – Graph functions as transformations of

MM3A2g – Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

GPS

An exponential decay function has the form y = abx , where a>0 and 0<b<1.

The base b of an exponential decay function is called the decay factor.

The time required for a substance to fall to half its initial value is called half-life.

Exponential Decay Model When a real-life quantity decreases by a fixed percent each year (or other time period), the amount y of the quantity after t years can be modeled by the equation y= a(1-r)t, where a is the initial amount and r is the percent decrease expressed as a decimal. Note that the quantity 1-r is the decay factor.

Vocabulary

What are some telling factors that the function is growth or decay?

What is Exponential Decay? Examples?

Graph

Steps: ◦ Make a table◦ Plot your points◦ Asymptote?◦ Domain & Range

Graph y=bx for 0 < b < 1

X -2 -1 0 1 2

Y

Graph

Steps: ◦ Make a table◦ Plot your points◦ Asymptote?◦ Domain & Range

Graph y=abx for 0 < b < 1

X -2 -1 0 1 2

Y

Graph

Steps: ◦ Make a table◦ Plot your points◦ Asymptote?◦ Domain & Range

Graph y=abx-h +k for 0 < b < 1

X -2 -1 0 1 2

Y

When a plant dies, it stops acquiring carbon-14 from the atmosphere. Carbon-14 decays over time with a half-life of about 5730 years. The percent P (in decimal form) of the original amount of carbon-14 that remains in a sample after t years is given by:

About how many years after a plant dies will 60% of the carbon-14 in the plant remain?

Using a half-life model

Half-Example

Try page 136: 3 & 4

Guided Practice Page

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