Exponential Functions and Ratios

The video tutorial explains how to determine the value of an exponential function m(x) at x=6. It begins by introducing the function and its form, m(x) = a * r^x, where a is the initial value and r is the common ratio. The initial value is identified as 9, and the common ratio is calculated as 1/3 using a table. The formula for m(x) is derived as 9 * (1/3)^x. Finally, the video demonstrates the calculation of m(6) by simplifying the expression to 1/81.

What is the main goal of the problem discussed in the video?

• To determine the common ratio

• To calculate m(6)

• To find the value of m(0)

• To draw the graph of the function

What form does the exponential function m(x) take?

• a / r^x

• a * r^x

• a - r^x

• a + r^x

What is the initial value 'a' in the function m(x)?

• 9

• 12

• 6

• 3

How is the common ratio 'r' determined from the table?

• By adding 3 to each value

• By multiplying by 1/3

• By subtracting 3 from each value

• By dividing by 3

What is the common ratio 'r' for the function m(x)?

• 1/2

• 1/5

• 1/3

• 1/4

What is the formula derived for m(x)?

• 9 * (1/3)^x

• 9 * (1/2)^x

• 9 * (1/4)^x

• 9 * (1/5)^x

What is the value of 3 to the 6th power?

• 81

• 729

• 243

• 6561

How is the expression for m(6) simplified?

• By subtracting 3 squared

• By adding 3 squared

• By dividing by 3 squared

• By multiplying by 3

What is the final value of m(6)?

• 1/729

• 1/243

• 1/81

• 1/27

What is the value of m(4) according to the table?

• 1/9

• 1/27

• 1/81

• 1/3