Decide whether the data in the table represent a linear function or an exponential function. explain how you know.
x y
1 162
2 54
3 18
4 6
5 2
a. the data represent an exponential function because there is a common ratio of 3.
b. the data represent a linear function because there is a common difference of 108.
c. the data represent a linear function because there is a common difference of –108.
d. the data represent an exponential function because there is a common ratio of 1/3.

Solution:

1. We will plot the points on the coordinate plane, if they lie in a line it means they are linear.

2. Find the slope between each two points ,if you don't want to plot these points on coordinate plane,then by using the formula of slope between two points which is , = ,if slopes are same between any two points it means these points are collinear.

As you can see in the coordinate plane that these points are not collinear.

Now ,

It means this is a geometric progression because

Option D : The data represent an exponential function because there is a common ratio of 1/3. is true statement.

a

step-by-step explanation:

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w