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?
o julia is correct because the distance starts at 5 feet and increases by a factor of 4.
o julia is correct because the function is true for (0, 5) and (1, 20).
o julia is not correct because the function is not true for the point (2, 80).
o julia is not correct because the distance does not increase by a constant factor each minute.

Explanation:

Step1: Check the function for (0, 5)

When \(x = 0\), \(y=5(4)^{0}=5\times1 = 5\)

Step2: Check the function for (1, 20)

When \(x = 1\), \(y = 5(4)^{1}=5\times4=20\)

Step3: Check the function for (2, 80)

When \(x = 2\), \(y=5(4)^{2}=5\times16 = 80\)

Step4: Check the function for (4, 320)

When \(x = 4\), \(y=5(4)^{4}=5\times256=1280
eq320\)

Step5: Check the function for (8, 640)

When \(x = 8\), \(y=5(4)^{8}=5\times65536 = 327680
eq640\)

Answer:

Julia is not correct because the function is not true for the point \((4,320)\) and \((8,640)\) (the closest option among the given ones is "Julia is not correct because the function is not true for the point \((2, 80)\)" which has a wrong - reasoning as the function is true for \((2,80)\) but overall the function does not model the data correctly due to the incorrect values for \(x = 4\) and \(x = 8\))