Question

PLEASE help!! Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function.
x

0

1

2

3

4


f (x)

12.5

13.75

15.125

16.638

18.301


a.

Exponential; y=12.5(1.10)^x


b.

Linear; y = 1.499x + 12.3648


c.

Exponential y=1.10(12.5)^x


d.

Linear; 12.3648x + 1.499

Answer 1

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:

$y=a(b)^x$

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,

$12.5=a(b)^0$

$12.5=a*1$ Since $b^0=1$

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,

$13.75=12.5(b)^1$

13.75=12.5b

$\frac{13.75}{12.5}=b$ 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,

$y=12.5(1.1)^x$

So, the correct choice is a.

Answer 2

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: