Question

Question 1 Given the following xy-chart. x-values y-values 0 5 1 35 2 245 3 1,715 4 12,005 5 84,035 What type of function is modeled? (1 point) Responses Linear Linear Exponential Exponential Quadratic Quadratic Question 2 Write the function for the above model using the data given in the xy-chart.(1 point) f(x)=

Answer 1

To determine the type of function modeled by the given xy-chart, let's analyze the data:

• The x-values are: 0, 1, 2, 3, 4, 5
• The corresponding y-values are: 5, 35, 245, 1,715, 12,005, 84,035

Question 1:

To figure out the type of function, we can look for patterns in the y-values as the x-values increase.

1. The y-values grow rapidly as x increases.
2. If you check the ratio of consecutive y-values:
   • 35/5 = 7
   • 245/35 = 7
   • 1715/245 = 7
   • 12005/1715 = 7
   • 84035/12005 = 7

The consistent ratio suggests that the function is exponential in nature.

Response: Exponential

Question 2:

We can express the function in the form \( f(x) = ab^x \), where:

• We can see that \( f(0) = 5 \) implies \( a = 5 \).
• The ratio between any two consecutive y-values is consistent with the formula \( f(x) = 5 \cdot 7^x \).

Now let's write the function using the data given:

Response: \( f(x) = 5 \cdot 7^x \)

In summary:

1. Type of function: Exponential
2. Function model: \( f(x) = 5 \cdot 7^x \)