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1.3.2: Creating and Graphing Exponential Equations

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1.3.2: Creating and Graphing Exponential Equations

Read the scenario and answer the questions that follow.

One form of the element beryllium, beryllium-11, has a half-life of about 14 seconds and decays to the element boron. A chemist starts out with 128 grams of beryllium-11. She monitors the element for 70 seconds.

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1. What is the equation that models the amount of beryllium-11 over time?

2. How many grams of beryllium-11 does the chemist have left after 70 seconds?

1. What is the equation that models the amount of beryllium-11 over time?• y = abx, where y is the final value, a is the initial

value, b is the rate of growth or decay, and x is the time.

y = unknown

a = 128 grams

b = 0.5

• Time = 70 seconds, but this needs to be converted to time periods before substituting the value for x.

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1.3.2: Creating and Graphing Exponential Equations

• Convert 70 seconds into 14-second time periods.

1 time period = 14 seconds

x = 5

• Substitute all the variables into the equation.

y = abx

y = 128(0.5)5

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1.3.2: Creating and Graphing Exponential Equations

2. How many grams of beryllium-11 does the chemist have left after 70 seconds?• Apply the order of operations to the equation from

the end of problem 1.

y = 128(0.5)5

y = 4 grams

1.3.2: Creating and Graphing Exponential Equations

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