Exponential Functions and Growth Rates

The video tutorial explains how to convert an exponential function into a form that uses a continuous growth rate. It starts by defining the exponential function F(t) = 40 * 1.20^t and aims to express it as G(t) = A * e^(Kt). The initial value A is identified, and the growth rate per unit time is calculated. The tutorial then demonstrates how to find the continuous growth rate K by using two points on the function and applying natural logarithms. Finally, it compares the original and converted functions to verify the calculations, highlighting the differences between discrete and continuous growth rates.

What does the value 'A' represent in the exponential function G(t) = A * e^(Kt)?

• The decay rate

• The initial value

• The time period

• The continuous growth rate

How is the exponential growth rate per unit of time calculated from the base in F(t)?

• By adding 1 to the base

• By subtracting 1 from the base

• By multiplying the base by 100

• By dividing the base by 2

What are the two points used to determine G(t) from F(t)?

• (0, 20) and (1, 24)

• (0, 40) and (1, 48)

• (0, 30) and (1, 36)

• (0, 50) and (1, 60)

What is the value of G(1) when determining G(t)?

• 0.1823

• 48

• 1.2

• 40

What mathematical operation is used to solve for K in the equation e^K = 1.2?

• Addition

• Subtraction

• Natural logarithm

• Exponentiation

What is the approximate value of the continuous growth rate K?

• 0.1623

• 0.1423

• 0.1823

• 0.2023

How does the continuous growth rate compare to the original growth rate per year?

• It is the same

• It is higher

• It is unrelated

• It is lower

What is the continuous growth rate expressed as a percentage?

• 10%

• 20%

• 18.23%

• 15%

Why might there be a slight difference in the table of values for the two functions?

• Due to rounding of K

• Due to incorrect calculations

• Due to different time units

• Due to different initial values

What is the purpose of comparing the table of values for Y1 and Y2?

• To verify the correctness of the conversion

• To find errors in the original function

• To determine the initial value

• To calculate the decay rate