At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
For the functions in this problem, we have that:
a) The function is exponential, and the table is completed as follows.
- x = 0: y = 1.
- x = 1: y = 5.
- x = 2: y = 25.
- x = 3: y = 125.
- x = 4: y = 625.
- x = 5: y = 3125.
b) The function is linear, and the table is completed as follows.
- x = 0: y = 0.
- x = 1: y = 5.
- x = 2: y = 10.
- x = 3: y = 15.
- x = 4: y = 20.
- x = 5: y = 25.
c) The function is exponential and given by:
[tex]y = -16\left(\frac{1}{2}\right)^x[/tex]
What is an exponential function?
An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
- a is the initial value.
- b is the rate of change.
A function with initial value 1 and where the y-value is computed by multiplied the previous y-value by 5, as in item a, is an exponential function with parameters a = 1 and b = 5, hence the rule is:
[tex]y = 5^x[/tex]
Then:
- x = 0: y = 1.
- x = 1: y = 5.
- x = 2: y = 25.
- x = 3: y = 125.
- x = 4: y = 625.
- x = 5: y = 3125.
What is a proportional relationship?
A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
A proportional relationship is also classified as linear with a intercept of 0. For item b, since each y-value is the x-value multiplied by 5, the rule is:
y = 5x.
Hence the table is:
- x = 0: y = 0.
- x = 1: y = 5.
- x = 2: y = 10.
- x = 3: y = 15.
- x = 4: y = 20.
- x = 5: y = 25.
For item c, when x changes by 1, y is always multiplied by 1/2, and due to the multiplication, the function is exponential and given by:
[tex]y = -16\left(\frac{1}{2}\right)^x[/tex]
The -16 is because when x = 0, y = -16.
More can be learned about functions at https://brainly.com/question/25537936
#SPJ1
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.