Exponential Functions Review

• Growth

• Decay

• Neither

Answer explanation

The equation y=3(1.5)^x represents exponential growth because the base (1.5) is greater than 1. As x increases, y will also increase, indicating growth.

2, 4, 8, 16, 32, 64... Is an example of exponential...

• Growth

• Decay

• Neither

Answer explanation

The sequence 2, 4, 8, 16, 32, 64 shows exponential growth, as each number is double the previous one. This indicates an increase over time, confirming that the correct answer is Growth.

• Growth

• Decay

• Neither

Answer explanation

The equation y=100(5)^x represents exponential growth because the base (5) is greater than 1. As x increases, y increases rapidly, indicating a growth pattern.

• Growth

• Decay

• Neither

Answer explanation

The function y = (1/3)^x represents exponential decay because the base (1/3) is less than 1. As x increases, y decreases, indicating that the value of y approaches zero, confirming it is a decay function.

What is this graph of?

• Growth

• Decay

• Neither

Answer explanation

The graph shows a decrease in values over time, indicating a decline. This pattern is characteristic of decay, making 'Decay' the correct choice.

• 3

• x

• f(x)

Answer explanation

The y-intercept occurs when x=0. Substituting x=0 into f(x)=\frac{1}{2}\cdot3^x gives f(0)=\frac{1}{2}\cdot3^0=\frac{1}{2}. Thus, the y-intercept is \frac{1}{2}.

• Growth

• Decay

• Neither

Answer explanation

The equation y=\frac{1}{3}x+10 represents a linear function with a positive slope (\frac{1}{3}), indicating growth. However, since the question asks for growth or decay, and the slope is not negative, the correct choice is 'Neither'.

What is shown in this graph?

• Growth

• Decay

• Neither

Answer explanation

The graph shows an upward trend, indicating an increase over time, which is characteristic of growth. Therefore, the correct answer is 'Growth'.

• Growth

• Decay

• Neither

Answer explanation

The function y = (2/3) * (3/4)^x has a base of 3/4, which is less than 1. This indicates exponential decay, as the value of y decreases as x increases.

• 3

• y

• x

Answer explanation

In the equation y=3⋅(1/2)^x, the starting value is represented by the coefficient of the term, which is 3. This indicates the initial value of y when x is 0.