Exponential Growth & Models

Which of the following represents an exponential growth function?

• f(x) = log(x)

• f(x) = 3^x

• f(x) = x^2

• f(x) = 2^x

What is the asymptotic behavior of an exponential function?

• Remains constant for all values of x

• Decreases as x approaches positive infinity

• Approaches zero as x approaches negative infinity and grows without bound as x approaches positive infinity.

• Has a linear growth pattern

How can exponential models be used to predict future values?

• By using linear regression analysis

• By ignoring the growth rate

• By randomly selecting values

• By fitting data to an exponential function and extrapolating the trend based on the growth rate.

Identify the exponential growth factor in the function f(x) = 2^x.

• 5

• 4

• 2

• 3

Explain the concept of doubling time in exponential growth.

• Doubling time = ln(2) / growth rate

• Doubling time = growth rate ^ 2

• Doubling time = growth rate / ln(2)

• Doubling time = growth rate * 2

In the function g(x) = 3^x, what happens to the values of g(x) as x approaches infinity?

• The values of g(x) will oscillate between positive and negative infinity as x approaches infinity.

• The values of g(x) will remain constant as x approaches infinity.

• The values of g(x) will approach infinity as x approaches infinity.

• The values of g(x) will approach zero as x approaches infinity.

What is the general form of an exponential function?

• f(x) = a * b * x

• f(x) = a + b^x

• f(x) = a * b^x

• f(x) = a * b + x

Calculate the value of e^3, where e is the base of the natural logarithm.

• 15.0855369232

• 22.0855369232

• 20.0855369232

• 18.2354369232

Describe the relationship between the base of an exponential function and its growth rate.

• The base of an exponential function determines its growth rate.

• The growth rate of an exponential function is determined by its exponent, not the base.

• Exponential functions with different bases always have the same growth rate.

• The base of an exponential function has no impact on its growth rate.

If an exponential function has a growth factor of 1.5, what does this indicate about its growth?

• The function's growth is by 50% for each unit increase in input.

• The function's growth is by 15% for each unit increase in input.

• The function's growth is by 1.5 units for each unit increase in input.

• The function's growth is by 150% for each unit increase in input.