Investment Functions and Rate of Change

The video tutorial explains how to calculate the average rate of change of an investment function, d(t) = 1000 * 2^(t/6), where t is the number of years after 2012. It covers the understanding of time variables, the application of the average rate of change formula, and the calculation of values at specific times. The tutorial concludes with the final calculation of the average rate of change between 2013 and 2015, emphasizing the importance of units in the result.

What is the initial value of the investment function given in the video?

• 500

• 2000

• 1000

• 1500

In the investment function, what does 't' represent?

• The number of months after 2012

• The number of years after 2012

• The number of weeks after 2012

• The number of days after 2012

What is the significance of the value 1000 in the investment function?

• It is the initial investment amount

• It is the final value

• It is the interest rate

• It is the time period

What is the base of the exponent in the investment function?

• 1

• 2

• 6

• 3

How many years after 2012 is the year 2013 represented in the function?

• 2

• 3

• 1

• 0

What is the value of 't' for the year 2015?

• 2

• 4

• 3

• 1

What is the formula used to calculate the average rate of change?

• (f(a) + f(b)) / 2

• (f(b) - f(a)) / (b - a)

• (f(b) - f(a)) * (b - a)

• (f(b) * f(a)) / (b + a)

What is the function value at t=3?

• 1414.21

• 1500.00

• 1122.46

• 1000.00

What is the purpose of using parentheses in the power calculation?

• To decrease the value

• To make the calculation faster

• To ensure correct order of operations

• To increase the value

What is the alternative way to express the power of 3/6?

• 0.3

• 0.6

• 0.5

• 0.8