x 0 1 2 3 4
f(x) 12.5 13.75 15.125 16.638 18.301
If the change in x values and change in y values are constant then the data will be linear.
So, change in x from 0 to 1 is 1-0=1
Similarly change in x from 1 to 2 is 2-1=1
So, change in x's is constant in the given data.
Now let's check for change in y values.
Change in y from 12.5 to 13.75 is 13.75-12.5=1.25
Similarly change in y from 13.75 to 15.125 is 15.125-13.75=1.375
Changes in y's are not constant.
So, the given data is not linear.
Let's assume the exponential function is:
[tex] y=a(b)^x [/tex]
Let's take any two points from the data and plug into the above equation to get the equation. Let's plug in the first point (0, 12.5) in the above function. So,
[tex] 12.5=a(b)^0 [/tex]
[tex] 12.5=a*1 [/tex] Since [tex] b^0=1 [/tex]
So, a=12.5
Next step is to plug in the second point (1, 13.75) and a=12.5 in the same equation to get the value of b. Hence,
[tex] 13.75=12.5(b)^1 [/tex]
13.75=12.5b
[tex] \frac{13.75}{12.5}=b [/tex] Dividing each sides by 12.5.
So, b=1.1
Now we can plug in the value of a and b to get the exponential formula. Hence,
[tex] y=12.5(1.1)^x [/tex]
So, the correct choice is a.
Answer:
f(x) 12.5 13.75 15.125 16.638 18.301
If the change in x values and change in y values are constant then the data will be linear.
So, change in x from 0 to 1 is 1-0=1
Similarly change in x from 1 to 2 is 2-1=1
So, change in x's is constant in the given data.
Now let's check for change in y values.
Change in y from 12.5 to 13.75 is 13.75-12.5=1.25
Similarly change in y from 13.75 to 15.125 is 15.125-13.75=1.375
Changes in y's are not constant.
So, the given data is not linear.
Step-by-step explanation:
