Exploring Exponential Growth and Decay

What is the primary reason for modeling certain phenomena with exponential functions?

• Because the quantity changes at a constant rate.

• Because exponential functions are easier to calculate.

• Because the rate of change depends on the current amount.

• Because it simplifies the phenomena into linear components.

Why does the number of people who know a rumor grow exponentially?

• Because each person tells the rumor to two more people.

• Because the rumor becomes more interesting over time.

• Because people are more likely to believe a rumor over time.

• Because the rate of spreading increases with the number of people who know it.

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CCSS.HSF.LE.A.2

What formula represents the number of people who know the rumor after a certain number of days?

• N = 3D^2

• N = 3 * 2^D

• N = 3D

• N = 3 + 2D

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CCSS.HSF.LE.A.4

After how many days will the number of people knowing the rumor exceed the population of the United States?

• 27 days

• 30 days

• 20 days

• 25 days

What does the formula 'N = 3 * 2^D' predict in the context of the rumor spreading example?

• The speed at which the rumor spreads.

• The number of rumors spread after D days.

• The total number of people who have heard the rumor after D days.

• The number of days it takes for 3 people to hear the rumor.

What is the initial distance between Helmut and the lighthouse?

• 40 feet

• 20 feet

• 160 feet

• 80 feet

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CCSS.6.EE.B.6

How far is Helmut from the lighthouse after 6 trips?

• 5 feet

• 2.5 feet

• 10 feet

• 1.25 feet

What concept does Helmut's approach to the lighthouse illustrate?

• Linear decay

• Exponential growth

• Exponential decay

• Quadratic decay

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CCSS.RI.6.1

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Why will Helmut never reach the lighthouse?

• Because he stops walking.

• Because he always has half the distance left to walk.

• Because the lighthouse moves away.

• Because he gets lost.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Why is the domain of the function only whole numbers?

• Because Helmut can only take whole number steps.

• Because the function cannot handle decimal values.

• Because Helmut only takes whole trips, not fractional ones.

• Because the lighthouse is only open on whole days.

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