Question

julia finds that the data in the table can be modeled by the function y = 5(4)^x. distance vs. time

time (minutes)	distance (feet)
1	20
2	80
4	320
8	640	which statement about julias finding is true? julia is correct because the distance starts at 5 feet and increases by a factor of 4. julia is correct because the function is true for (0, 5) and (1, 20). julia is not correct because the function is not true for the point (2, 80). julia is not correct because the distance does not increase by a constant factor each minute.

Explanation:

Step1: Check the function for point (0, 5)

Substitute \(x = 0\) into \(y=5(4)^{x}\), we get \(y = 5\times4^{0}=5\times1 = 5\)

Step2: Check the function for point (1, 20)

Substitute \(x = 1\) into \(y = 5(4)^{x}\), we get \(y=5\times4^{1}=5\times4 = 20\)

Step3: Check the function for point (2, 80)

Substitute \(x = 2\) into \(y = 5(4)^{x}\), we get \(y=5\times4^{2}=5\times16 = 80\)

Step4: Analyze the growth factor

The function \(y = 5(4)^{x}\) is an exponential - growth function with a growth factor of 4. The distance values in the table also increase by a factor of 4 each time the time is incremented by 1 unit.

Answer:

Julia is correct because the function is true for \((0,5)\) and \((1,20)\)