Study Guide for Exponential Functions

• A

• B

• C

• D

When multiplying powers of the same base, such as (3²)(3), you will _____________ the exponents.

• Add

• Subtract

• Multiply

• Divide

When raising a power to a power, such as (6³)⁵ you will __________ the exponents.

• Add

• Subtract

• Multiply

• Divide

If (2^x)⁵=2¹⁵, what does x equal?

• x = 3

• x = 5

• x = 10

Answer explanation

Simplify the expression:

• 3⁷⁰

• 3¹³

• 3¹⁷

• 3³⁰

Answer explanation

How is the growth rate determined for an exponential function?

• By the value of the base

• By the value of the constant term

• By the value of the coefficient

• By the value of the exponent

Answer explanation

The growth rate of an exponential function is determined by the value of the base. In an exponential function, the base is raised to a power, and the growth rate depends on how much the base increases or decreases when the exponent changes.

Describe the significance of initial value in exponential functions.

• The initial value in exponential functions is the starting point or the value of the function when the input is zero.

• The initial value in exponential functions is the value of the function when the input is one.

• The initial value in exponential functions is the average value of the function.

• The initial value in exponential functions is the maximum value of the function.

Answer explanation

The significance of the initial value in exponential functions lies in its role as the starting point or the value of the function when the input is zero.

In an exponential function, what does the 'a' represent? 

• SLOPE

• RATE OF CHANGE

• STARTING VALUE (y-intercept)

• GROWTH OR DECAY FACTOR

Answer explanation

In an exponential function, 'a' represents the starting value or the y-intercept. This is the value of the function when the input is zero. It's not the slope, rate of change, or growth/decay factor. These are different aspects of the function. The starting value is the point where the function starts on the y-axis.

In an exponential function, what does the 'b' represent?

• SLOPE

• RATE OF CHANGE

• STARTING VALUE (y-intercept)

• GROWTH OR DECAY  FACTOR

Answer explanation

In an exponential function, 'b' represents the 'Growth or Decay Factor'. This means that 'b' is the factor by which the function grows or decays for each unit increase in the x-value. It is not the slope, rate of change, or the starting value (y-intercept).

What does the graph represent?

• Exponential Decay

• Exponential Growth

Answer explanation

The question asks about the type of growth represented by the graph. The correct answer is 'Exponential Decay'. This indicates that the values in the graph are decreasing at a rate proportional to their current value, which is a characteristic of exponential decay.