Exponential Functions and Growth Rates

The video tutorial explains how to convert an exponential function with base e into a form with a different base. It starts by defining the initial value and continuous growth rate, then explains how to find the growth rate per unit of time. The tutorial uses function values to perform the conversion and calculates the new base. Finally, it verifies the calculations using a graphing calculator, ensuring the accuracy of the conversion.

What is the initial value A in the exponential function F(t) = 100e^(0.2t)?

• 100

• 200

• 50

• 150

What does the coefficient 0.2 in the function F(t) = 100e^(0.2t) represent?

• Base value

• Decay rate

• Continuous growth rate

• Initial value

In the function G(t) = A * B^t, what does B - 1 represent?

• Initial value

• Continuous growth rate

• Growth rate per unit time

• Decay rate

What is the value of F(0) in the function F(t) = 100e^(0.2t)?

• 0

• 100

• 200

• 50

What is the approximate value of F(1) in the function F(t) = 100e^(0.2t)?

• 100

• 110

• 122.14

• 150

How do you calculate the base B in the function G(t) = 100 * B^t?

• Subtract 100 from 122.1403

• Divide 122.1403 by 100

• Multiply 100 by 122.1403

• Divide 100 by 122.1403

What is the calculated base B for the function G(t) = 100 * B^t?

• 2.0

• 0.8

• 1.2214

• 1.5

What is the growth rate per year if T is in years for the function G(t) = 100 * 1.2214^t?

• 20%

• 30%

• 22.14%

• 25%

What feature of the graphing calculator is used to compare the function values of F(t) and G(t)?

• Equation solver

• Graph feature

• Table feature

• Matrix calculator

Why might there be a slight difference in the values of Y1 and Y2 when comparing F(t) and G(t)?

• Incorrect initial value

• Rounding of base B

• Wrong function input

• Calculator error