Exploring Exponential Functions Quiz 03/2025

How do we know that is an example of an exponential growth?

• Its a line going up

• Its a line going down

• Its a smooth curve going down

• Its a smooth curve going up

Answer explanation

Exponential growth is characterized by a smooth curve going up, indicating that the quantity increases rapidly over time. This distinguishes it from linear or decreasing trends, making the correct choice 'It's a smooth curve going up'.

• Exponential Growth

• Exponential Decay

• Quadratic

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• A straight line passing through the origin.

• A curve that increases rapidly and passes through the point (0, 1).

• A parabola opening upwards.

• A horizontal line.

Answer explanation

The correct graph for the exponential function y = 2^x is a curve that increases rapidly, starting at (0, 1) since 2^0 = 1. This distinguishes it from straight lines, parabolas, and horizontal lines.

Identify the exponential growth function from the following options:

Answer explanation

The exponential growth function is characterized by a constant base raised to a variable exponent. Among the options, y = 5^x fits this definition, as it shows exponential growth with base 5.

Which of the following equations represents exponential decay?

Answer explanation

The equation y = 0.5^x represents exponential decay because the base (0.5) is less than 1, causing the value of y to decrease as x increases. The other options represent growth or different types of functions.

Answer explanation

The population doubles every hour, which is an exponential growth model. The correct function is P(t) = 100 * 2^t, where 100 is the initial population and 2^t represents the doubling every hour.

Which of the following is a real-world example of exponential growth?

• The depreciation of a car's value over time.

• The spread of a viral video on social media.

• The cooling of a hot beverage.

• The linear increase in salary with years of experience.

Answer explanation

The spread of a viral video on social media exemplifies exponential growth, as each viewer can share it with many others, leading to rapid increases in views, unlike the other options which depict linear or diminishing trends.

Answer explanation

The substance decays at 3% per year, meaning 97% remains each year. The model A(t) = A_0 * (0.97)^t correctly represents this exponential decay, while the other options do not reflect the decay rate accurately.

Which of the following graphs represents an exponential decay function?

• A curve that decreases rapidly and approaches the x-axis.

• A straight line with a negative slope.

• A parabola opening downwards.

• A horizontal line.

Answer explanation

An exponential decay function is characterized by a curve that decreases rapidly and approaches the x-axis, indicating that the value gets closer to zero but never actually reaches it. This matches the correct choice.