NC Math Exponential

The two graphs show models characterized by exponential decay representing the area covered by two different algae blooms, in square yards, weeks after different chemicals were applied.

Which algae bloom covered a larger area when the chemicals were applied?

• Algae shown by red triangles

• Algae shown by blue circles

Which algae population is decreasing more rapidly?

• Algae shown by red triangles

• Algae shown by blue circles

What is the weekly growth factor for the insect population?

• 9

• 3

• 1/3

• 1/9

Answer explanation

Be careful - the two points given are for weeks 1 and 3 -not successive weeks.

A bee population is measured each week, and the results are plotted on the graph. What is an equation that models the bee population, b, w weeks after it is first measured?

log₂(¹/₈) = -3

• 2^-3 = ¹/₈

• 2^1/8 = -3

• -3² = ¹/₈

• -3^1/8 = 2

A population of migrating butterflies, p, is observed for w weeks since they began their migration.

Given the data, what is the factor of growth or decay of the butterfly population?

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Answer explanation

b(4) = 810,000

Interpretation:

4 days after the population of bacteria was 10,000, the population of bacteria was 810,000.

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The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

• y=8(15,000)^x

• y=15,000(1.08)^x

• y=15,000(0.92)^x

• y=15,000(0.08)^x

What is a, the initial amount, for the function: f(x) = 300(1.16)^x?

• 300

• 1.16

• .16

• x