Question

(03.05 mc) aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. to prepare for the event, she is practicing and keeping track of her time to complete each station. the x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. (1, 3), (2, 6), (3, 12), (4, 24) part a: is this data modeling a linear function or an exponential function? explain your answer. (2 points) part b: write a function to represent the data. show your work. (4 points) part c: determine the average rate of change between day 2 and day 4. show your work. (4 points)

Answer 1

a. The data represents an exponential function, as the outputs have equal ratios.

b. The function is: $y = 1.5(2)^x$

c. The rate of change between day 2 and day 4 is of 9.

What is an exponential function?

An exponential function is modeled according to the following rule:

$y = a(b)^x$

In which the parameters are described below:

• a is the initial value of the function, that is, the value of y when x = 0.

• b is the rate of change of the function, representing the constant ratio between the outputs.

For the points given in this problem, the constant ratio is given by:

b = 24/12 = 12/6 = 6/3 = 2.

Due to this constant ratio, it is an exponential function and not a linear function.

Applying recursion, the initial value can be found as follows:

y(1) = 2y(0)

3 = 2a

a = 1.5

Hence the rule for the function is:

$y = 1.5(2)^x$

The rate of change between days 2 and 4 is found as follows:

• f(2) = 6.

• f(4) = 24.

Hence:

r = (24 - 6)/(4 - 2) = 18/2 = 9.

More can be learned about exponential functions at https://brainly.com/question/25537936

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