Question

please help, need answer fast!
Julia finds that the data in the table can be modeled by the function y = 5(4)x.


Which statement about Julia’s 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.

Answer 1

we are given

$y=5(4)^x$

we will verify each options

option-A:

At x=0

$y=5(4)^0$

$y=5\times 1$

$y=5$

So, it starts at 5

and it's factor is 4

so, this is TRUE

option-B:

Julia is correct for all values

so, this is FALSE

option-C:

At x=2 ,

$y=5(4)^2$

$y=5\times 16$

$y=80$

so, Julia is correct for (2,80) as well

so, this is FALSE

option-D:

we can see that

constant growth factor =4

so, this is FALSE

Answer 2

A function assigns the value of each element of one set to the other specific element of another set. The correct option is D.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

As per the given table and the given function y = 5(4)ˣ. If we substitute the value and check the function, as shown below,

When x = 0,

y = 5(4)⁰ = 5

When x = 1,

y = 5(4)¹ = 20

When x = 2,

y = 5(4)² = 80

When x = 4,

y = 5(4)⁴ = 1280

When x = 8,

y = 5(4)⁸ = 327,680

Since the value does not satisfy each value of the table, therefore, it can be concluded that Julia is not correct because the distance does not increase by a constant factor each minute.

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