Exploring Exponential Functions and Their Applications

What is the general form of an exponential function?

• f(x) = a + bx

• f(x) = a * b^x

• f(x) = ax / b

• f(x) = a - b^x

What does the parameter 'a' in an exponential function represent?

• The x-intercept

• The common ratio

• The slope of the graph

• The y-intercept

What does the y-intercept of an exponential function graphically represent?

• The rate of change of the function

• The slope at the origin

• The maximum value of the function

• The starting value of the function

What is the significance of the y-intercept in the context of exponential functions?

• It determines the slope of the function

• It indicates the highest value of y

• It represents the initial value of the function

• It shows the rate at which y decreases

If the y-values in a table are 3, 9, 27, what is the value of 'b'?

• 3

• 9

• 27

• 6

How is the common ratio 'b' determined from a sequence of y-values like 4, 8, 16?

• By subtracting 4 each time

• By multiplying by 2

• By dividing by 2

• By adding 4 each time

If the y-values in a sequence are decreasing by half each time, what is the value of 'b'?

• 1

• -1

• 2

• 0.5

In a scientific experiment, if the amount of bacteria triples every hour, what is the value of 'b'?

• 5

• 4

• 3

• 2

What is the correct exponential function for a sequence starting at 70 and tripling every period?

• y = 70 * 3^t

• y = 70 * 2^t

• y = 70 + 3t

• y = 70 - 3^t

In the matching exercise, which function corresponds to a y-intercept of -1?

• First function

• Second function

• Third function

• Fourth function