Question

Use the table to answer the question.
x-values Y-values
0 5
1 35
2 245
3 1715
4 12005
5 84035


Given the following xy
-chart, create a function model. Does this illustrate a linear function, an exponential function, or a quadratic function to represent the dataset?

(1 point)
Responses

f(x)=7(5)^x
and exponential function
f of x is equal to 7 times 5 to the x th power and exponential function

f(x)=5(7)^x
and exponential function
f of x is equal to 5 times 7 to the x th power and exponential function

f(x)=5(7)^x
and quadratic function
f of x is equal to 5 times 7 to the x th power and quadratic function

f(x)=5x+30
and linear function

Answer 1

To determine the appropriate function model for the given dataset, we first analyze the growth of the y-values as the x-values increase.

Looking at the changes in the y-values:

- From 0 to 1: 5 to 35 (increases by 30)
- From 1 to 2: 35 to 245 (increases by 210)
- From 2 to 3: 245 to 1715 (increases by 1470)
- From 3 to 4: 1715 to 12005 (increases by 10290)
- From 4 to 5: 12005 to 84035 (increases by 72030)

The increases are not constant, which indicates that it is not a linear function.

Next, let's look at whether the function could be exponential or quadratic. In an exponential function, the ratio of successive y-values tends to be constant (or increases at a constant rate), while in a quadratic function, the second differences of the y-values tend to be constant.

Calculating the ratios:

- 35 / 5 = 7
- 245 / 35 = 7
- 1715 / 245 = 7
- 12005 / 1715 ≈ 7
- 84035 / 12005 ≈ 7

Since the ratio of successive y-values is consistent and appears to be approximately 7, this suggests that the function is indeed exponential.

Based on the options given, the function that fits the data well is:

**f(x) = 5(7)^x** and it represents an exponential function.

The correct choice would therefore be:
**f(x)=5(7)^x and exponential function.**