Question

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

Substitute \(x = 0\) into \(y=5(4)^{x}\). We get \(y = 5(4)^{0}=5\times1 = 5\).

Step2: Check the function for (1, 20)

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

Step3: Check the function for (2, 80)

Substitute \(x = 2\) into \(y = 5(4)^{x}\). We get \(y=5(4)^{2}=5\times16 = 80\).

Step4: Analyze the growth factor

The general form of an exponential function is \(y = a(b)^{x}\), where \(a\) is the initial - value and \(b\) is the growth factor. Here \(a = 5\) and \(b = 4\), which means the distance starts at 5 feet and increases by a factor of 4 each time.

Answer:

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